Id	Statement	Proof	Names
0	→𝜑→𝜓𝜑	Axiom	ax-1
1	→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Axiom	ax-2
2	→→¬𝜑¬𝜓→𝜓𝜑	Axiom	ax-3, con4
3	¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Axiom	df-bi
4	↔⋀𝜑𝜓¬→𝜑¬𝜓	Axiom	df-an
5	→𝜑→𝜑𝜑	Subs [𝜓↗𝜑] into ax-1
6	→𝜑→→𝜑𝜑𝜑	Subs [𝜓↗→𝜑𝜑] into ax-1
7	→→𝜑→→𝜑𝜑𝜑→→𝜑→𝜑𝜑→𝜑𝜑	Subs [𝜓↗→𝜑𝜑, 𝜒↗𝜑] into ax-2
8	→→𝜑→𝜑𝜑→𝜑𝜑	Modus ponens 6, 7
9	→𝜑𝜑	Modus ponens 5, 8	id
10	→𝜓𝜓	Subs [𝜑↗𝜓] into id
11	→→𝜓𝜓→𝜑→𝜓𝜓	Subs [𝜑↗→𝜓𝜓, 𝜓↗𝜑] into ax-1
12	→𝜑→𝜓𝜓	Modus ponens 10, 11	idd
13	→𝜑→𝜒𝜑	Subs [𝜓↗𝜒] into ax-1
14	→→𝜑→𝜒𝜑→𝜑→𝜑→𝜒𝜑	Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗𝜑] into ax-1
15	→𝜑→𝜑→𝜒𝜑	Modus ponens 13, 14
16	→→𝜑→𝜑→𝜒𝜑→→𝜑𝜑→𝜑→𝜒𝜑	Subs [𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2
17	→→𝜑𝜑→𝜑→𝜒𝜑	Modus ponens 15, 16
18	→→𝜒𝜑→𝜓→𝜒𝜑	Subs [𝜑↗→𝜒𝜑] into ax-1
19	→→→𝜒𝜑→𝜓→𝜒𝜑→𝜑→→𝜒𝜑→𝜓→𝜒𝜑	Subs [𝜑↗→→𝜒𝜑→𝜓→𝜒𝜑, 𝜓↗𝜑] into ax-1
20	→𝜑→→𝜒𝜑→𝜓→𝜒𝜑	Modus ponens 18, 19
21	→→𝜑→→𝜒𝜑→𝜓→𝜒𝜑→→𝜑→𝜒𝜑→𝜑→𝜓→𝜒𝜑	Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜓→𝜒𝜑] into ax-2
22	→→𝜑→𝜒𝜑→𝜑→𝜓→𝜒𝜑	Modus ponens 20, 21
23	→𝜑→𝜓→𝜒𝜑	Modus ponens 13, 22	2a1
24	→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓] into id
25	→𝜑→→𝜑𝜓𝜑	Subs [𝜓↗→𝜑𝜓] into ax-1
26	→→𝜑→→𝜑𝜓𝜑→𝜑→𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
27	→𝜑→𝜑→→𝜑𝜓𝜑	Modus ponens 25, 26
28	→→𝜑→𝜑→→𝜑𝜓𝜑→→𝜑𝜑→𝜑→→𝜑𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2
29	→→𝜑𝜑→𝜑→→𝜑𝜓𝜑	Modus ponens 27, 28
30	→→→𝜑𝜓→𝜑𝜓→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
31	→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Modus ponens 24, 30
32	→→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
33	→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Modus ponens 31, 32
34	→→𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜑→𝜑→→𝜑𝜓𝜓	Subs [𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2
35	→→𝜑→→𝜑𝜓𝜑→𝜑→→𝜑𝜓𝜓	Modus ponens 33, 34
36	→𝜑→→𝜑𝜓𝜓	Modus ponens 25, 35	pm2.27
37	→→𝜑→→𝜑𝜓𝜓→→𝜑→𝜑𝜓→𝜑𝜓	Subs [𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
38	→→𝜑→𝜑𝜓→𝜑𝜓	Modus ponens pm2.27, 37	pm2.43
39	→→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into ax-1
40	→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
41	→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 39, 40
42	→→→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
43	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 41, 42
44	→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
45	→→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓	Subs [𝜑↗→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
46	→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓	Modus ponens 44, 45
47	→→→𝜑𝜓→→𝜒→𝜑𝜓→→𝜒𝜑→𝜒𝜓→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒𝜑→𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→→𝜒𝜑→𝜒𝜓] into ax-2
48	→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒𝜑→𝜒𝜓	Modus ponens 46, 47
49	→→𝜑𝜓→→𝜒𝜑→𝜒𝜓	Modus ponens 39, 48	imim2
50	→→𝜑𝜓→𝜒𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into idd
51	→→𝜒𝜒→𝜓→𝜒𝜒	Subs [𝜑↗→𝜒𝜒] into ax-1
52	→→→𝜒𝜒→𝜓→𝜒𝜒→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗→𝜑𝜓] into ax-1
53	→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒	Modus ponens 51, 52
54	→→→𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜓→𝜒𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
55	→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜓→𝜒𝜒	Modus ponens 53, 54
56	→→𝜑𝜓→𝜓→𝜒𝜒	Modus ponens 50, 55
57	→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into ax-2
58	→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
59	→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Modus ponens 57, 58
60	→→→𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→→𝜑𝜓→𝜓→𝜒𝜒→→𝜑𝜓→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
61	→→→𝜑𝜓→𝜓→𝜒𝜒→→𝜑𝜓→→𝜓𝜒→𝜓𝜒	Modus ponens 59, 60
62	→→𝜑𝜓→→𝜓𝜒→𝜓𝜒	Modus ponens 56, 61
63	→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-1
64	→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
65	→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 63, 64
66	→→→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
67	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 65, 66
68	→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imim2
69	→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
70	→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 68, 69
71	→→→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
72	→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 70, 71
73	→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
74	→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 72, 73
75	→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
76	→→→𝜑𝜓→→𝜓𝜒→𝜓𝜒→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 74, 75
77	→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 62, 76
78	→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
79	→→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
80	→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 78, 79
81	→→→𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2
82	→→→𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 80, 81
83	→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 77, 82
84	→→→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
85	→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 83, 84
86	→→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 63, 85	imim1
87	→→𝜓𝜒→→𝜒𝜃→𝜓𝜃	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into imim1
88	→→→𝜓𝜒→→𝜒𝜃→𝜓𝜃→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃	Subs [𝜑↗→→𝜓𝜒→→𝜒𝜃→𝜓𝜃, 𝜓↗𝜑] into ax-1
89	→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃	Modus ponens 87, 88
90	→→𝜑→→𝜓𝜒→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃	Subs [𝜓↗→𝜓𝜒, 𝜒↗→→𝜒𝜃→𝜓𝜃] into ax-2
91	→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃	Modus ponens 89, 90
92	→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃	Subs [𝜓↗→𝜒𝜃, 𝜒↗→𝜓𝜃] into ax-2
93	→→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃	Subs [𝜑↗→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃, 𝜓↗→𝜑→𝜓𝜒] into ax-1
94	→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃	Modus ponens 92, 93
95	→→→𝜑→𝜓𝜒→→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜒𝜃→𝜑→𝜓𝜃→→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→→𝜒𝜃→𝜓𝜃, 𝜒↗→→𝜑→𝜒𝜃→𝜑→𝜓𝜃] into ax-2
96	→→→𝜑→𝜓𝜒→𝜑→→𝜒𝜃→𝜓𝜃→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃	Modus ponens 94, 95
97	→→𝜑→𝜓𝜒→→𝜑→𝜒𝜃→𝜑→𝜓𝜃	Modus ponens 91, 96	pm2.83
98	→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imim1
99	→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑𝜑] into id
100	→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
101	→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑	Modus ponens 99, 100
102	→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
103	→→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
104	→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑	Modus ponens 102, 103
105	→→→→𝜑𝜓𝜒→→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑] into ax-2
106	→→→→𝜑𝜓𝜒→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑	Modus ponens 104, 105
107	→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑	Modus ponens 98, 106
108	→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into imim2
109	→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
110	→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Modus ponens 108, 109
111	→→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑] into ax-2
112	→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Modus ponens 110, 111
113	→→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
114	→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Modus ponens 112, 113
115	→→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑] into ax-2
116	→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Modus ponens 114, 115
117	→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑	Modus ponens 101, 116
118	→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→𝜒𝜑𝜑] into ax-2
119	→→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
120	→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Modus ponens 118, 119
121	→→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑, 𝜒↗→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑] into ax-2
122	→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→→𝜒𝜑→→𝜑𝜓𝜑→→𝜒𝜑𝜑→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Modus ponens 120, 121
123	→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Modus ponens 117, 122
124	→→→→𝜑𝜓𝜒→→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑, 𝜒↗→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑] into ax-2
125	→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Modus ponens 123, 124
126	→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑	Modus ponens 107, 125
127	→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-1
128	→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
129	→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑	Modus ponens 127, 128
130	→→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑] into ax-2
131	→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑	Modus ponens 129, 130
132	→→→→𝜑𝜓𝜒→→→→𝜑𝜓𝜑𝜑→→𝜒𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→→𝜑𝜓𝜑𝜑, 𝜒↗→→𝜒𝜑𝜑] into ax-2
133	→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑	Modus ponens 126, 132
134	→→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑	Subs [𝜑↗→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜑𝜑] into ax-1
135	→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑	Modus ponens 133, 134
136	→→→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑, 𝜒↗→→→𝜑𝜓𝜒→→𝜒𝜑𝜑] into ax-2
137	→→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑	Modus ponens 135, 136
138	→→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜒→→𝜒𝜑𝜑	Modus ponens 127, 137	peirceroll
139	→→𝜑→𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒] into id
140	→𝜓→→𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm2.27
141	→→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒	Subs [𝜑↗→𝜓→→𝜓𝜒𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
142	→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒	Modus ponens 140, 141
143	→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒] into ax-1
144	→→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
145	→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒	Modus ponens 143, 144
146	→→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜓→𝜑→𝜓𝜒] into ax-2
147	→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒	Modus ponens 145, 146
148	→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗𝜒, 𝜒↗𝜑] into imim2
149	→→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1
150	→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 148, 149
151	→→𝜓→→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜓𝜒𝜒, 𝜒↗→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
152	→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 150, 151
153	→→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
154	→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 152, 153
155	→→→𝜑→𝜓𝜒→→𝜓→→𝜓𝜒𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→→𝜓𝜒𝜒, 𝜒↗→𝜓→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
156	→→→𝜑→𝜓𝜒→𝜓→→𝜓𝜒𝜒→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 154, 155
157	→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 142, 156
158	→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
159	→→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Subs [𝜑↗→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
160	→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Modus ponens 158, 159
161	→→→𝜑→𝜓𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒] into ax-2
162	→→→𝜑→𝜓𝜒→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Modus ponens 160, 161
163	→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Modus ponens 157, 162
164	→→→𝜑→𝜓𝜒→→𝜓→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→𝜑→𝜓𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2
165	→→→𝜑→𝜓𝜒→𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Modus ponens 163, 164
166	→→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Modus ponens 143, 165	pm2.04
167	→→𝜒𝜃→→𝜓𝜒→𝜓𝜃	Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into imim2
168	→→𝜑𝜓→→𝜓𝜃→𝜑𝜃	Subs [𝜒↗𝜃] into imim1
169	→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃	Subs [𝜑↗→→𝜑𝜓→→𝜓𝜃→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1
170	→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃	Modus ponens 168, 169
171	→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃	Subs [𝜑↗→→𝜓𝜒→𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
172	→→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃	Subs [𝜑↗→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃, 𝜓↗→𝜒𝜃] into ax-1
173	→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃	Modus ponens 171, 172
174	→→→𝜒𝜃→→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→→𝜒𝜃→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜑𝜓→→𝜓𝜒→𝜓𝜃] into ax-2
175	→→→𝜒𝜃→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃	Modus ponens 173, 174
176	→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃	Modus ponens 167, 175
177	→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜓𝜃, 𝜓↗→𝜑𝜃, 𝜒↗→𝜓𝜒] into imim2
178	→→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜑𝜓] into ax-1
179	→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 177, 178
180	→→→𝜑𝜓→→→𝜓𝜃→𝜑𝜃→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜃→𝜑𝜃, 𝜒↗→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃] into ax-2
181	→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 179, 180
182	→→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1
183	→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 181, 182
184	→→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→𝜓𝜃→𝜑𝜃, 𝜒↗→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃] into ax-2
185	→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜃→𝜑𝜃→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 183, 184
186	→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 170, 185
187	→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜓𝜒→𝜑𝜃] into ax-2
188	→→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜒𝜃] into ax-1
189	→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Modus ponens 187, 188
190	→→→𝜒𝜃→→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃, 𝜒↗→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃] into ax-2
191	→→→𝜒𝜃→→𝜑𝜓→→→𝜓𝜒→𝜓𝜃→→𝜓𝜒→𝜑𝜃→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Modus ponens 189, 190
192	→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Modus ponens 186, 191
193	→→→𝜒𝜃→→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓→→𝜓𝜒→𝜓𝜃, 𝜒↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜃] into ax-2
194	→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜓𝜃→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Modus ponens 192, 193
195	→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃	Modus ponens 176, 194
196	→→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into ax-1
197	→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
198	→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Modus ponens 196, 197
199	→→→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜒𝜃→𝜑𝜓] into ax-2
200	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Modus ponens 198, 199
201	→→→𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜃→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜃] into ax-2
202	→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 195, 201
203	→→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃, 𝜓↗→𝜑𝜓] into ax-1
204	→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 202, 203
205	→→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→→𝜓𝜒→𝜑𝜃] into ax-2
206	→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 204, 205
207	→→𝜑𝜓→→𝜒𝜃→→𝜓𝜒→𝜑𝜃	Modus ponens 196, 206	imim12
208	→𝜓→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-1
209	→𝜒𝜒	Subs [𝜑↗𝜒] into id
210	→→𝜒𝜒→→𝜑𝜓→𝜒𝜒	Subs [𝜑↗→𝜒𝜒, 𝜓↗→𝜑𝜓] into ax-1
211	→→→𝜑𝜓→𝜒𝜒→→→𝜑𝜓𝜒→→𝜑𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into ax-2
212	→→→𝜑𝜓𝜒→→𝜑𝜓𝜒	Modus ponens 50, 211
213	→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜒] into ax-1
214	→→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓] into ax-1
215	→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 213, 214
216	→→𝜓→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒→𝜑𝜓] into ax-2
217	→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 215, 216
218	→𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 208, 217
219	→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-2
220	→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒	Modus ponens 212, 219
221	→→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒	Subs [𝜑↗→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒] into ax-1
222	→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒	Modus ponens 220, 221
223	→→𝜓→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→→𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→→𝜑𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗→→→𝜑𝜓𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒𝜒] into ax-2
224	→→𝜓→→→𝜑𝜓𝜒→𝜑𝜓→𝜓→→→𝜑𝜓𝜒𝜒	Modus ponens 222, 223
225	→𝜓→→→𝜑𝜓𝜒𝜒	Modus ponens 218, 224
226	→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒	Subs [𝜑↗→→𝜑𝜓𝜒] into ax-1
227	→→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
228	→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒	Modus ponens 226, 227
229	→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓𝜒] into ax-2
230	→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒	Modus ponens 228, 229
231	→→𝜓→→→𝜑𝜓𝜒𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓𝜒] into ax-2
232	→→𝜓→→𝜑𝜓𝜒→𝜓𝜒	Modus ponens 225, 231
233	→→→𝜓→→𝜑𝜓𝜒→𝜓𝜒→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜓→→𝜑𝜓𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
234	→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒	Modus ponens 232, 233
235	→→→→𝜑𝜓𝜒→→𝜓→→𝜑𝜓𝜒→𝜓𝜒→→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→𝜓→→𝜑𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
236	→→→→𝜑𝜓𝜒→𝜓→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→𝜓𝜒	Modus ponens 234, 235
237	→→→𝜑𝜓𝜒→𝜓𝜒	Modus ponens 226, 236	jarr
238	→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒] into id
239	→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
240	→→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-1
241	→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 239, 240
242	→→𝜓→→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2
243	→→𝜓→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 241, 242
244	→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 208, 243
245	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
246	→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 238, 245
247	→→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-1
248	→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 246, 247
249	→→𝜓→→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2
250	→→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 248, 249
251	→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 244, 250
252	→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒] into ax-1
253	→→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
254	→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒	Modus ponens 252, 253
255	→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→→𝜑𝜓→𝜑𝜒] into ax-2
256	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒	Modus ponens 254, 255
257	→→𝜓→→→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜒] into ax-2
258	→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 251, 257
259	→→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Subs [𝜑↗→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
260	→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 258, 259
261	→→→→𝜑𝜓→𝜑𝜒→→𝜓→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2
262	→→→→𝜑𝜓→𝜑𝜒→𝜓→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 260, 261
263	→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 252, 262
264	→𝜑→→𝜑𝜒𝜒	Subs [𝜓↗𝜒] into pm2.27
265	→→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒	Subs [𝜑↗→𝜑→→𝜑𝜒𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
266	→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒	Modus ponens 264, 265
267	→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Subs [𝜑↗→𝜓→𝜑𝜒, 𝜓↗𝜑] into ax-1
268	→→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Subs [𝜑↗→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
269	→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Modus ponens 267, 268
270	→→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓→𝜑𝜒] into ax-2
271	→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Modus ponens 269, 270
272	→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Modus ponens 263, 271
273	→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
274	→→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
275	→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 273, 274
276	→→𝜑→→→𝜑𝜒𝜒→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2
277	→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 275, 276
278	→→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
279	→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 277, 278
280	→→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2
281	→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 279, 280
282	→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 266, 281
283	→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜓𝜒] into ax-2
284	→→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
285	→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 283, 284
286	→→→→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜒↗→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒] into ax-2
287	→→→→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 285, 286
288	→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 282, 287
289	→→→→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
290	→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 288, 289
291	→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 272, 290	pm2.86
292	→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑	Subs [𝜒↗→𝜓𝜑] into jarr
293	→→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜓	Subs [𝜑↗→𝜓𝜓, 𝜓↗→→𝜑𝜓→𝜓𝜑] into ax-1
294	→→→𝜑𝜓→𝜓𝜑→𝜓𝜓	Modus ponens 10, 293
295	→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑	Subs [𝜑↗𝜓, 𝜒↗𝜑] into ax-2
296	→→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑	Subs [𝜑↗→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑, 𝜓↗→→𝜑𝜓→𝜓𝜑] into ax-1
297	→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑	Modus ponens 295, 296
298	→→→→𝜑𝜓→𝜓𝜑→→𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑	Subs [𝜑↗→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓→𝜓𝜑, 𝜒↗→→𝜓𝜓→𝜓𝜑] into ax-2
299	→→→→𝜑𝜓→𝜓𝜑→𝜓→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑	Modus ponens 297, 298
300	→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑	Modus ponens 292, 299
301	→→→→𝜑𝜓→𝜓𝜑→→𝜓𝜓→𝜓𝜑→→→→𝜑𝜓→𝜓𝜑→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜑	Subs [𝜑↗→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜓, 𝜒↗→𝜓𝜑] into ax-2
302	→→→→𝜑𝜓→𝜓𝜑→𝜓𝜓→→→𝜑𝜓→𝜓𝜑→𝜓𝜑	Modus ponens 300, 301
303	→→→𝜑𝜓→𝜓𝜑→𝜓𝜑	Modus ponens 294, 302	loolin
304	→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-2
305	→→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
306	→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 304, 305
307	→→→→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→→𝜓𝜑→𝜓𝜒] into ax-2
308	→→→→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 306, 307
309	→→→𝜑𝜓→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 263, 308	loowoz
310	→¬𝜑¬𝜑	Subs [𝜑↗¬𝜑] into id
311	→¬𝜑→¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into ax-1
312	→→¬𝜑→¬𝜓¬𝜑→¬𝜑→¬𝜑→¬𝜓¬𝜑	Subs [𝜑↗→¬𝜑→¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
313	→¬𝜑→¬𝜑→¬𝜓¬𝜑	Modus ponens 311, 312
314	→→¬𝜑→¬𝜑→¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2
315	→→¬𝜑¬𝜑→¬𝜑→¬𝜓¬𝜑	Modus ponens 313, 314
316	→→¬𝜓¬𝜑→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into ax-3
317	→→→¬𝜓¬𝜑→𝜑𝜓→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓	Subs [𝜑↗→→¬𝜓¬𝜑→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
318	→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓	Modus ponens 316, 317
319	→→¬𝜑→→¬𝜓¬𝜑→𝜑𝜓→→¬𝜑→¬𝜓¬𝜑→¬𝜑→𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
320	→→¬𝜑→¬𝜓¬𝜑→¬𝜑→𝜑𝜓	Modus ponens 318, 319
321	→¬𝜑→𝜑𝜓	Modus ponens 311, 320	pm2.21
322	→𝜑→¬𝜑𝜑	Subs [𝜓↗¬𝜑] into ax-1
323	→→𝜑→¬𝜑𝜑→𝜑→𝜑→¬𝜑𝜑	Subs [𝜑↗→𝜑→¬𝜑𝜑, 𝜓↗𝜑] into ax-1
324	→𝜑→𝜑→¬𝜑𝜑	Modus ponens 322, 323
325	→→𝜑→𝜑→¬𝜑𝜑→→𝜑𝜑→𝜑→¬𝜑𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬𝜑𝜑] into ax-2
326	→→𝜑𝜑→𝜑→¬𝜑𝜑	Modus ponens 324, 325
327	→→¬𝜑→𝜑𝜓→→¬𝜑𝜑→¬𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
328	→→¬𝜑𝜑→¬𝜑𝜓	Modus ponens pm2.21, 327
329	→→→¬𝜑𝜑→¬𝜑𝜓→𝜑→→¬𝜑𝜑→¬𝜑𝜓	Subs [𝜑↗→→¬𝜑𝜑→¬𝜑𝜓, 𝜓↗𝜑] into ax-1
330	→𝜑→→¬𝜑𝜑→¬𝜑𝜓	Modus ponens 328, 329
331	→→𝜑→→¬𝜑𝜑→¬𝜑𝜓→→𝜑→¬𝜑𝜑→𝜑→¬𝜑𝜓	Subs [𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑𝜓] into ax-2
332	→→𝜑→¬𝜑𝜑→𝜑→¬𝜑𝜓	Modus ponens 330, 331
333	→𝜑→¬𝜑𝜓	Modus ponens 322, 332	pm2.24
334	→→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
335	→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 213, 334
336	→→¬𝜑→→𝜑𝜓→→→𝜑𝜓𝜒→𝜑𝜓→→¬𝜑→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒→𝜑𝜓] into ax-2
337	→→¬𝜑→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 335, 336
338	→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓	Modus ponens pm2.21, 337
339	→→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒	Subs [𝜑↗→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒, 𝜓↗¬𝜑] into ax-1
340	→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒	Modus ponens 220, 339
341	→→¬𝜑→→→→𝜑𝜓𝜒→𝜑𝜓→→→𝜑𝜓𝜒𝜒→→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→→→𝜑𝜓𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜒𝜒] into ax-2
342	→→¬𝜑→→→𝜑𝜓𝜒→𝜑𝜓→¬𝜑→→→𝜑𝜓𝜒𝜒	Modus ponens 340, 341
343	→¬𝜑→→→𝜑𝜓𝜒𝜒	Modus ponens 338, 342
344	→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗¬𝜑] into ax-1
345	→→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
346	→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒	Modus ponens 344, 345
347	→→→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→¬𝜑→→𝜑𝜓𝜒] into ax-2
348	→→→→𝜑𝜓𝜒→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒	Modus ponens 346, 347
349	→→¬𝜑→→→𝜑𝜓𝜒𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓𝜒] into ax-2
350	→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒	Modus ponens 343, 349
351	→→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒	Subs [𝜑↗→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒, 𝜓↗→→𝜑𝜓𝜒] into ax-1
352	→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒	Modus ponens 350, 351
353	→→→→𝜑𝜓𝜒→→¬𝜑→→𝜑𝜓𝜒→¬𝜑𝜒→→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑𝜒	Subs [𝜑↗→→𝜑𝜓𝜒, 𝜓↗→¬𝜑→→𝜑𝜓𝜒, 𝜒↗→¬𝜑𝜒] into ax-2
354	→→→→𝜑𝜓𝜒→¬𝜑→→𝜑𝜓𝜒→→→𝜑𝜓𝜒→¬𝜑𝜒	Modus ponens 352, 353
355	→→→𝜑𝜓𝜒→¬𝜑𝜒	Modus ponens 344, 354	jarl
356	→→¬𝜑𝜑→¬𝜑𝜑	Subs [𝜑↗→¬𝜑𝜑] into id
357	→¬𝜑→𝜑¬→¬𝜑𝜑	Subs [𝜓↗¬→¬𝜑𝜑] into pm2.21
358	→→¬𝜑→𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑	Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗¬→¬𝜑𝜑] into ax-2
359	→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑	Modus ponens 357, 358
360	→→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑	Subs [𝜑↗→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑] into ax-1
361	→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑	Modus ponens 359, 360
362	→→→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑	Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑¬→¬𝜑𝜑] into ax-2
363	→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑	Modus ponens 361, 362
364	→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑	Subs [𝜓↗→¬𝜑𝜑] into ax-3
365	→→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑	Subs [𝜑↗→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑, 𝜓↗→¬𝜑𝜑] into ax-1
366	→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑	Modus ponens 364, 365
367	→→→¬𝜑𝜑→→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑𝜑→→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑𝜑	Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑¬→¬𝜑𝜑, 𝜒↗→→¬𝜑𝜑𝜑] into ax-2
368	→→→¬𝜑𝜑→¬𝜑¬→¬𝜑𝜑→→¬𝜑𝜑→→¬𝜑𝜑𝜑	Modus ponens 366, 367
369	→→¬𝜑𝜑→→¬𝜑𝜑𝜑	Modus ponens 359, 368
370	→→→¬𝜑𝜑→→¬𝜑𝜑𝜑→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑𝜑	Subs [𝜑↗→¬𝜑𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗𝜑] into ax-2
371	→→→¬𝜑𝜑→¬𝜑𝜑→→¬𝜑𝜑𝜑	Modus ponens 369, 370
372	→→¬𝜑𝜑𝜑	Modus ponens 356, 371	pm2.18
373	→¬¬𝜑→¬𝜑𝜑	Subs [𝜑↗¬𝜑, 𝜓↗𝜑] into pm2.21
374	→→→¬𝜑𝜑𝜑→¬¬𝜑→→¬𝜑𝜑𝜑	Subs [𝜑↗→→¬𝜑𝜑𝜑, 𝜓↗¬¬𝜑] into ax-1
375	→¬¬𝜑→→¬𝜑𝜑𝜑	Modus ponens pm2.18, 374
376	→→¬¬𝜑→→¬𝜑𝜑𝜑→→¬¬𝜑→¬𝜑𝜑→¬¬𝜑𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗𝜑] into ax-2
377	→→¬¬𝜑→¬𝜑𝜑→¬¬𝜑𝜑	Modus ponens 375, 376
378	→¬¬𝜑𝜑	Modus ponens 373, 377	notnotr
379	→→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓] into id
380	→𝜑→→𝜑¬𝜓𝜑	Subs [𝜓↗→𝜑¬𝜓] into ax-1
381	→→𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑	Subs [𝜑↗→𝜑→→𝜑¬𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1
382	→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑	Modus ponens 380, 381
383	→→¬¬𝜑→𝜑→→𝜑¬𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→→𝜑¬𝜓𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑¬𝜓𝜑] into ax-2
384	→→¬¬𝜑𝜑→¬¬𝜑→→𝜑¬𝜓𝜑	Modus ponens 382, 383
385	→¬¬𝜑→→𝜑¬𝜓𝜑	Modus ponens notnotr, 384
386	→→→𝜑¬𝜓→𝜑¬𝜓→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗¬𝜓] into ax-2
387	→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓	Modus ponens 379, 386
388	→→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓	Subs [𝜑↗→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓, 𝜓↗¬¬𝜑] into ax-1
389	→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓	Modus ponens 387, 388
390	→→¬¬𝜑→→→𝜑¬𝜓𝜑→→𝜑¬𝜓¬𝜓→→¬¬𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→→𝜑¬𝜓¬𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗→→𝜑¬𝜓𝜑, 𝜒↗→→𝜑¬𝜓¬𝜓] into ax-2
391	→→¬¬𝜑→→𝜑¬𝜓𝜑→¬¬𝜑→→𝜑¬𝜓¬𝜓	Modus ponens 389, 390
392	→¬¬𝜑→→𝜑¬𝜓¬𝜓	Modus ponens 385, 391
393	→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬𝜑] into ax-1
394	→→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
395	→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓	Modus ponens 393, 394
396	→→→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→¬¬𝜑→𝜑¬𝜓] into ax-2
397	→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓	Modus ponens 395, 396
398	→→¬¬𝜑→→𝜑¬𝜓¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬𝜓] into ax-2
399	→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓	Modus ponens 392, 398
400	→→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓	Subs [𝜑↗→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
401	→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓	Modus ponens 399, 400
402	→→→𝜑¬𝜓→→¬¬𝜑→𝜑¬𝜓→¬¬𝜑¬𝜓→→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬¬𝜑→𝜑¬𝜓, 𝜒↗→¬¬𝜑¬𝜓] into ax-2
403	→→→𝜑¬𝜓→¬¬𝜑→𝜑¬𝜓→→𝜑¬𝜓→¬¬𝜑¬𝜓	Modus ponens 401, 402
404	→→𝜑¬𝜓→¬¬𝜑¬𝜓	Modus ponens 393, 403
405	→→¬¬𝜑¬𝜓→𝜓¬𝜑	Subs [𝜑↗¬𝜑] into ax-3
406	→→→¬¬𝜑¬𝜓→𝜓¬𝜑→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑	Subs [𝜑↗→→¬¬𝜑¬𝜓→𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
407	→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑	Modus ponens 405, 406
408	→→→𝜑¬𝜓→→¬¬𝜑¬𝜓→𝜓¬𝜑→→→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬¬𝜑¬𝜓, 𝜒↗→𝜓¬𝜑] into ax-2
409	→→→𝜑¬𝜓→¬¬𝜑¬𝜓→→𝜑¬𝜓→𝜓¬𝜑	Modus ponens 407, 408
410	→→𝜑¬𝜓→𝜓¬𝜑	Modus ponens 404, 409	con2
411	→→¬𝜑¬𝜑→𝜑→¬𝜑¬𝜑	Subs [𝜑↗→¬𝜑¬𝜑, 𝜓↗𝜑] into ax-1
412	→𝜑→¬𝜑¬𝜑	Modus ponens 310, 411
413	→¬¬¬𝜑¬𝜑	Subs [𝜑↗¬𝜑] into notnotr
414	→¬𝜑→𝜑¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗𝜑] into ax-1
415	→→¬𝜑→𝜑¬𝜑→¬¬¬𝜑→¬𝜑→𝜑¬𝜑	Subs [𝜑↗→¬𝜑→𝜑¬𝜑, 𝜓↗¬¬¬𝜑] into ax-1
416	→¬¬¬𝜑→¬𝜑→𝜑¬𝜑	Modus ponens 414, 415
417	→→¬¬¬𝜑→¬𝜑→𝜑¬𝜑→→¬¬¬𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑	Subs [𝜑↗¬¬¬𝜑, 𝜓↗¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2
418	→→¬¬¬𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑	Modus ponens 416, 417
419	→¬¬¬𝜑→𝜑¬𝜑	Modus ponens 413, 418
420	→→𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→𝜑¬𝜑	Subs [𝜓↗¬𝜑, 𝜒↗¬𝜑] into ax-2
421	→→𝜑¬𝜑→𝜑¬𝜑	Modus ponens 412, 420
422	→→→𝜑¬𝜑→𝜑¬𝜑→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑	Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜑, 𝜓↗¬¬¬𝜑] into ax-1
423	→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑	Modus ponens 421, 422
424	→→¬¬¬𝜑→→𝜑¬𝜑→𝜑¬𝜑→→¬¬¬𝜑→𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑	Subs [𝜑↗¬¬¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2
425	→→¬¬¬𝜑→𝜑¬𝜑→¬¬¬𝜑→𝜑¬𝜑	Modus ponens 423, 424
426	→𝜑→¬¬¬𝜑𝜑	Subs [𝜓↗¬¬¬𝜑] into ax-1
427	→→𝜑→¬¬¬𝜑𝜑→𝜑→𝜑→¬¬¬𝜑𝜑	Subs [𝜑↗→𝜑→¬¬¬𝜑𝜑, 𝜓↗𝜑] into ax-1
428	→𝜑→𝜑→¬¬¬𝜑𝜑	Modus ponens 426, 427
429	→→𝜑→𝜑→¬¬¬𝜑𝜑→→𝜑𝜑→𝜑→¬¬¬𝜑𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬¬𝜑𝜑] into ax-2
430	→→𝜑𝜑→𝜑→¬¬¬𝜑𝜑	Modus ponens 428, 429
431	→→¬¬¬𝜑→𝜑¬𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑	Subs [𝜑↗¬¬¬𝜑, 𝜓↗𝜑, 𝜒↗¬𝜑] into ax-2
432	→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑	Modus ponens 419, 431
433	→→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑	Subs [𝜑↗→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑, 𝜓↗𝜑] into ax-1
434	→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑	Modus ponens 432, 433
435	→→𝜑→→¬¬¬𝜑𝜑→¬¬¬𝜑¬𝜑→→𝜑→¬¬¬𝜑𝜑→𝜑→¬¬¬𝜑¬𝜑	Subs [𝜓↗→¬¬¬𝜑𝜑, 𝜒↗→¬¬¬𝜑¬𝜑] into ax-2
436	→→𝜑→¬¬¬𝜑𝜑→𝜑→¬¬¬𝜑¬𝜑	Modus ponens 434, 435
437	→𝜑→¬¬¬𝜑¬𝜑	Modus ponens 426, 436
438	→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑] into ax-3
439	→→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑	Subs [𝜑↗→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑, 𝜓↗𝜑] into ax-1
440	→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑	Modus ponens 438, 439
441	→→𝜑→→¬¬¬𝜑¬𝜑→𝜑¬¬𝜑→→𝜑→¬¬¬𝜑¬𝜑→𝜑→𝜑¬¬𝜑	Subs [𝜓↗→¬¬¬𝜑¬𝜑, 𝜒↗→𝜑¬¬𝜑] into ax-2
442	→→𝜑→¬¬¬𝜑¬𝜑→𝜑→𝜑¬¬𝜑	Modus ponens 440, 441
443	→𝜑→𝜑¬¬𝜑	Modus ponens 437, 442
444	→→𝜑→𝜑¬¬𝜑→→𝜑𝜑→𝜑¬¬𝜑	Subs [𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
445	→→𝜑𝜑→𝜑¬¬𝜑	Modus ponens 443, 444
446	→𝜑¬¬𝜑	Modus ponens id, 445	notnot
447	→→¬𝜑𝜓→¬𝜑𝜓	Subs [𝜑↗→¬𝜑𝜓] into id
448	→𝜓¬¬𝜓	Subs [𝜑↗𝜓] into notnot
449	→→𝜓¬¬𝜓→¬𝜑→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1
450	→¬𝜑→𝜓¬¬𝜓	Modus ponens 448, 449
451	→→¬𝜑→𝜓¬¬𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓	Subs [𝜑↗¬𝜑, 𝜒↗¬¬𝜓] into ax-2
452	→→¬𝜑𝜓→¬𝜑¬¬𝜓	Modus ponens 450, 451
453	→→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓	Subs [𝜑↗→→¬𝜑𝜓→¬𝜑¬¬𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
454	→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓	Modus ponens 452, 453
455	→→→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗→¬𝜑¬¬𝜓] into ax-2
456	→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→¬𝜑¬¬𝜓	Modus ponens 454, 455
457	→→¬𝜑¬¬𝜓→¬𝜓𝜑	Subs [𝜓↗¬𝜓] into ax-3
458	→→→¬𝜑¬¬𝜓→¬𝜓𝜑→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑	Subs [𝜑↗→→¬𝜑¬¬𝜓→¬𝜓𝜑, 𝜓↗→¬𝜑𝜓] into ax-1
459	→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑	Modus ponens 457, 458
460	→→→¬𝜑𝜓→→¬𝜑¬¬𝜓→¬𝜓𝜑→→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→¬𝜓𝜑	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑¬¬𝜓, 𝜒↗→¬𝜓𝜑] into ax-2
461	→→→¬𝜑𝜓→¬𝜑¬¬𝜓→→¬𝜑𝜓→¬𝜓𝜑	Modus ponens 459, 460
462	→→¬𝜑𝜓→¬𝜓𝜑	Modus ponens 452, 461	con1
463	→→𝜑→→𝜑𝜓𝜑→¬¬𝜑→𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1
464	→¬¬𝜑→𝜑→→𝜑𝜓𝜑	Modus ponens 25, 463
465	→→¬¬𝜑→𝜑→→𝜑𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→→𝜑𝜓𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2
466	→→¬¬𝜑𝜑→¬¬𝜑→→𝜑𝜓𝜑	Modus ponens 464, 465
467	→¬¬𝜑→→𝜑𝜓𝜑	Modus ponens notnotr, 466
468	→→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗¬¬𝜑] into ax-1
469	→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Modus ponens 31, 468
470	→→¬¬𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→¬¬𝜑→→𝜑𝜓𝜑→¬¬𝜑→→𝜑𝜓𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2
471	→→¬¬𝜑→→𝜑𝜓𝜑→¬¬𝜑→→𝜑𝜓𝜓	Modus ponens 469, 470
472	→¬¬𝜑→→𝜑𝜓𝜓	Modus ponens 467, 471
473	→→𝜑𝜓→¬¬𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬𝜑] into ax-1
474	→→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→¬¬𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
475	→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓	Modus ponens 473, 474
476	→→→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬𝜑→𝜑𝜓] into ax-2
477	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜑→𝜑𝜓	Modus ponens 475, 476
478	→→¬¬𝜑→→𝜑𝜓𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
479	→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓	Modus ponens 472, 478
480	→→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓	Subs [𝜑↗→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
481	→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓	Modus ponens 479, 480
482	→→→𝜑𝜓→→¬¬𝜑→𝜑𝜓→¬¬𝜑𝜓→→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→¬¬𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑→𝜑𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2
483	→→→𝜑𝜓→¬¬𝜑→𝜑𝜓→→𝜑𝜓→¬¬𝜑𝜓	Modus ponens 481, 482
484	→→𝜑𝜓→¬¬𝜑𝜓	Modus ponens 473, 483
485	→→𝜓¬¬𝜓→¬¬𝜑→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜑] into ax-1
486	→¬¬𝜑→𝜓¬¬𝜓	Modus ponens 448, 485
487	→→¬¬𝜑→𝜓¬¬𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗¬¬𝜑, 𝜒↗¬¬𝜓] into ax-2
488	→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 486, 487
489	→→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓, 𝜓↗→𝜑𝜓] into ax-1
490	→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 488, 489
491	→→→𝜑𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
492	→→→𝜑𝜓→¬¬𝜑𝜓→→𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 490, 491
493	→→𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 484, 492
494	→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into ax-3
495	→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗→𝜑𝜓] into ax-1
496	→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Modus ponens 494, 495
497	→→→𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→→𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→¬𝜓¬𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
498	→→→𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜑𝜓→¬𝜓¬𝜑	Modus ponens 496, 497
499	→→𝜑𝜓→¬𝜓¬𝜑	Modus ponens 493, 498	con3
500	→𝜑→→𝜑¬𝜓¬𝜓	Subs [𝜓↗¬𝜓] into pm2.27
501	→¬¬→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓] into notnotr
502	→→𝜑¬𝜓→𝜑→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗𝜑] into ax-1
503	→→→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬𝜓→𝜑→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into ax-1
504	→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓	Modus ponens 502, 503
505	→→¬¬→𝜑¬𝜓→→𝜑¬𝜓→𝜑→𝜑¬𝜓→→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓	Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑→𝜑¬𝜓] into ax-2
506	→→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓	Modus ponens 504, 505
507	→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓	Modus ponens 501, 506
508	→→𝜑→→𝜑¬𝜓¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜓↗→𝜑¬𝜓, 𝜒↗¬𝜓] into ax-2
509	→→𝜑→𝜑¬𝜓→𝜑¬𝜓	Modus ponens 500, 508
510	→→→𝜑→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗→→𝜑→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into ax-1
511	→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓	Modus ponens 509, 510
512	→→¬¬→𝜑¬𝜓→→𝜑→𝜑¬𝜓→𝜑¬𝜓→→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
513	→→¬¬→𝜑¬𝜓→𝜑→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓	Modus ponens 511, 512
514	→𝜑→¬¬→𝜑¬𝜓𝜑	Subs [𝜓↗¬¬→𝜑¬𝜓] into ax-1
515	→→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑	Subs [𝜑↗→𝜑→¬¬→𝜑¬𝜓𝜑, 𝜓↗𝜑] into ax-1
516	→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑	Modus ponens 514, 515
517	→→𝜑→𝜑→¬¬→𝜑¬𝜓𝜑→→𝜑𝜑→𝜑→¬¬→𝜑¬𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬→𝜑¬𝜓𝜑] into ax-2
518	→→𝜑𝜑→𝜑→¬¬→𝜑¬𝜓𝜑	Modus ponens 516, 517
519	→→¬¬→𝜑¬𝜓→𝜑¬𝜓→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓	Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗¬𝜓] into ax-2
520	→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓	Modus ponens 501, 519
521	→→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓	Subs [𝜑↗→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1
522	→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓	Modus ponens 520, 521
523	→→𝜑→→¬¬→𝜑¬𝜓𝜑→¬¬→𝜑¬𝜓¬𝜓→→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→¬¬→𝜑¬𝜓¬𝜓	Subs [𝜓↗→¬¬→𝜑¬𝜓𝜑, 𝜒↗→¬¬→𝜑¬𝜓¬𝜓] into ax-2
524	→→𝜑→¬¬→𝜑¬𝜓𝜑→𝜑→¬¬→𝜑¬𝜓¬𝜓	Modus ponens 522, 523
525	→𝜑→¬¬→𝜑¬𝜓¬𝜓	Modus ponens 514, 524
526	→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓] into ax-3
527	→→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓, 𝜓↗𝜑] into ax-1
528	→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓	Modus ponens 526, 527
529	→→𝜑→→¬¬→𝜑¬𝜓¬𝜓→𝜓¬→𝜑¬𝜓→→𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→𝜓¬→𝜑¬𝜓	Subs [𝜓↗→¬¬→𝜑¬𝜓¬𝜓, 𝜒↗→𝜓¬→𝜑¬𝜓] into ax-2
530	→→𝜑→¬¬→𝜑¬𝜓¬𝜓→𝜑→𝜓¬→𝜑¬𝜓	Modus ponens 528, 529
531	→𝜑→𝜓¬→𝜑¬𝜓	Modus ponens 525, 530	pm3.2im
532	→¬¬→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓] into notnotr
533	→→𝜑𝜓→𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑] into ax-1
534	→→→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
535	→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓	Modus ponens 533, 534
536	→→¬¬→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜑→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into ax-2
537	→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜑→𝜑𝜓	Modus ponens 535, 536
538	→¬¬→𝜑𝜓→𝜑→𝜑𝜓	Modus ponens 532, 537
539	→→→𝜑→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
540	→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓	Modus ponens pm2.43, 539
541	→→¬¬→𝜑𝜓→→𝜑→𝜑𝜓→𝜑𝜓→→¬¬→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
542	→→¬¬→𝜑𝜓→𝜑→𝜑𝜓→¬¬→𝜑𝜓→𝜑𝜓	Modus ponens 540, 541
543	→𝜑→¬¬→𝜑𝜓𝜑	Subs [𝜓↗¬¬→𝜑𝜓] into ax-1
544	→→𝜑→¬¬→𝜑𝜓𝜑→𝜑→𝜑→¬¬→𝜑𝜓𝜑	Subs [𝜑↗→𝜑→¬¬→𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
545	→𝜑→𝜑→¬¬→𝜑𝜓𝜑	Modus ponens 543, 544
546	→→𝜑→𝜑→¬¬→𝜑𝜓𝜑→→𝜑𝜑→𝜑→¬¬→𝜑𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬→𝜑𝜓𝜑] into ax-2
547	→→𝜑𝜑→𝜑→¬¬→𝜑𝜓𝜑	Modus ponens 545, 546
548	→→¬¬→𝜑𝜓→𝜑𝜓→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
549	→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓	Modus ponens 532, 548
550	→→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
551	→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓	Modus ponens 549, 550
552	→→𝜑→→¬¬→𝜑𝜓𝜑→¬¬→𝜑𝜓𝜓→→𝜑→¬¬→𝜑𝜓𝜑→𝜑→¬¬→𝜑𝜓𝜓	Subs [𝜓↗→¬¬→𝜑𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓𝜓] into ax-2
553	→→𝜑→¬¬→𝜑𝜓𝜑→𝜑→¬¬→𝜑𝜓𝜓	Modus ponens 551, 552
554	→𝜑→¬¬→𝜑𝜓𝜓	Modus ponens 543, 553
555	→→𝜓¬¬𝜓→¬¬→𝜑𝜓→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
556	→¬¬→𝜑𝜓→𝜓¬¬𝜓	Modus ponens 448, 555
557	→→¬¬→𝜑𝜓→𝜓¬¬𝜓→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜒↗¬¬𝜓] into ax-2
558	→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓	Modus ponens 556, 557
559	→→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
560	→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓	Modus ponens 558, 559
561	→→𝜑→→¬¬→𝜑𝜓𝜓→¬¬→𝜑𝜓¬¬𝜓→→𝜑→¬¬→𝜑𝜓𝜓→𝜑→¬¬→𝜑𝜓¬¬𝜓	Subs [𝜓↗→¬¬→𝜑𝜓𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬𝜓] into ax-2
562	→→𝜑→¬¬→𝜑𝜓𝜓→𝜑→¬¬→𝜑𝜓¬¬𝜓	Modus ponens 560, 561
563	→𝜑→¬¬→𝜑𝜓¬¬𝜓	Modus ponens 554, 562
564	→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-3
565	→→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓, 𝜓↗𝜑] into ax-1
566	→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓	Modus ponens 564, 565
567	→→𝜑→→¬¬→𝜑𝜓¬¬𝜓→¬𝜓¬→𝜑𝜓→→𝜑→¬¬→𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬→𝜑𝜓	Subs [𝜓↗→¬¬→𝜑𝜓¬¬𝜓, 𝜒↗→¬𝜓¬→𝜑𝜓] into ax-2
568	→→𝜑→¬¬→𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬→𝜑𝜓	Modus ponens 566, 567
569	→𝜑→¬𝜓¬→𝜑𝜓	Modus ponens 563, 568	jcn
570	→¬¬𝜓𝜓	Subs [𝜑↗𝜓] into notnotr
571	→→𝜓→𝜑𝜓→¬¬𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
572	→¬¬𝜓→𝜓→𝜑𝜓	Modus ponens 208, 571
573	→→¬¬𝜓→𝜓→𝜑𝜓→→¬¬𝜓𝜓→¬¬𝜓→𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜒↗→𝜑𝜓] into ax-2
574	→→¬¬𝜓𝜓→¬¬𝜓→𝜑𝜓	Modus ponens 572, 573
575	→¬¬𝜓→𝜑𝜓	Modus ponens 570, 574
576	→→𝜑→𝜓𝜓→→𝜑𝜓→𝜑𝜓	Subs [𝜒↗𝜓] into ax-2
577	→→→𝜑𝜓→𝜑𝜓→¬¬𝜓→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
578	→¬¬𝜓→→𝜑𝜓→𝜑𝜓	Modus ponens 24, 577
579	→→¬¬𝜓→→𝜑𝜓→𝜑𝜓→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
580	→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜓	Modus ponens 578, 579
581	→𝜑→¬¬𝜓𝜑	Subs [𝜓↗¬¬𝜓] into ax-1
582	→→𝜑→¬¬𝜓𝜑→𝜑→𝜑→¬¬𝜓𝜑	Subs [𝜑↗→𝜑→¬¬𝜓𝜑, 𝜓↗𝜑] into ax-1
583	→𝜑→𝜑→¬¬𝜓𝜑	Modus ponens 581, 582
584	→→𝜑→𝜑→¬¬𝜓𝜑→→𝜑𝜑→𝜑→¬¬𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬𝜓𝜑] into ax-2
585	→→𝜑𝜑→𝜑→¬¬𝜓𝜑	Modus ponens 583, 584
586	→→¬¬𝜓→𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
587	→→¬¬𝜓𝜑→¬¬𝜓𝜓	Modus ponens 575, 586
588	→→→¬¬𝜓𝜑→¬¬𝜓𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓𝜓, 𝜓↗𝜑] into ax-1
589	→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓	Modus ponens 587, 588
590	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜓	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓𝜓] into ax-2
591	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜓	Modus ponens 589, 590
592	→𝜑→¬¬𝜓𝜓	Modus ponens 581, 591
593	→→𝜓¬¬𝜓→¬¬𝜓→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1
594	→¬¬𝜓→𝜓¬¬𝜓	Modus ponens 448, 593
595	→→¬¬𝜓→𝜓¬¬𝜓→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓	Subs [𝜑↗¬¬𝜓, 𝜒↗¬¬𝜓] into ax-2
596	→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓	Modus ponens 594, 595
597	→→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓	Subs [𝜑↗→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
598	→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓	Modus ponens 596, 597
599	→→𝜑→→¬¬𝜓𝜓→¬¬𝜓¬¬𝜓→→𝜑→¬¬𝜓𝜓→𝜑→¬¬𝜓¬¬𝜓	Subs [𝜓↗→¬¬𝜓𝜓, 𝜒↗→¬¬𝜓¬¬𝜓] into ax-2
600	→→𝜑→¬¬𝜓𝜓→𝜑→¬¬𝜓¬¬𝜓	Modus ponens 598, 599
601	→𝜑→¬¬𝜓¬¬𝜓	Modus ponens 592, 600
602	→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓] into ax-3
603	→→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1
604	→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓	Modus ponens 602, 603
605	→→𝜑→→¬¬𝜓¬¬𝜓→¬𝜓¬𝜓→→𝜑→¬¬𝜓¬¬𝜓→𝜑→¬𝜓¬𝜓	Subs [𝜓↗→¬¬𝜓¬¬𝜓, 𝜒↗→¬𝜓¬𝜓] into ax-2
606	→→𝜑→¬¬𝜓¬¬𝜓→𝜑→¬𝜓¬𝜓	Modus ponens 604, 605
607	→𝜑→¬𝜓¬𝜓	Modus ponens 601, 606
608	→¬𝜓¬𝜓	Subs [𝜑↗¬𝜓] into id
609	→¬𝜓→𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗𝜑] into ax-1
610	→→¬𝜓→𝜑¬𝜓→¬𝜓→¬𝜓→𝜑¬𝜓	Subs [𝜑↗→¬𝜓→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
611	→¬𝜓→¬𝜓→𝜑¬𝜓	Modus ponens 609, 610
612	→→¬𝜓→¬𝜓→𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
613	→→¬𝜓¬𝜓→¬𝜓→𝜑¬𝜓	Modus ponens 611, 612
614	→→𝜑→¬𝜓¬𝜓→→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜓↗¬𝜓, 𝜒↗¬𝜓] into ax-2
615	→→→𝜑¬𝜓→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
616	→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓	Modus ponens 379, 615
617	→→¬𝜓→→𝜑¬𝜓→𝜑¬𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
618	→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬𝜓	Modus ponens 616, 617
619	→¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓] into id
620	→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
621	→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 619, 620
622	→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓] into notnotr
623	→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
624	→→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
625	→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Modus ponens 623, 624
626	→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬𝜓¬→𝜑¬𝜓] into ax-2
627	→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Modus ponens 625, 626
628	→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Modus ponens 622, 627
629	→→¬𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
630	→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Modus ponens 621, 629
631	→→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
632	→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Modus ponens 630, 631
633	→→¬¬¬→𝜑¬𝜓→→¬𝜓¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬𝜓¬→𝜑¬𝜓, 𝜒↗→¬𝜓¬→𝜑¬𝜓] into ax-2
634	→→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓	Modus ponens 632, 633
635	→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
636	→→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
637	→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓	Modus ponens 635, 636
638	→→¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬𝜓] into ax-2
639	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓	Modus ponens 637, 638
640	→→¬¬¬→𝜑¬𝜓→¬𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
641	→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 628, 640
642	→→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
643	→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 641, 642
644	→→¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
645	→→¬𝜓→¬¬¬→𝜑¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 643, 644
646	→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 635, 645
647	→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-3
648	→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
649	→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 647, 648
650	→→¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
651	→→¬𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 649, 650
652	→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 646, 651
653	→→¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
654	→→¬𝜓→𝜑¬𝜓→¬𝜓¬¬→𝜑¬𝜓	Modus ponens 652, 653
655	→¬𝜓¬¬→𝜑¬𝜓	Modus ponens 609, 654
656	→→¬𝜓¬¬→𝜑¬𝜓→¬→𝜑¬𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-3
657	→¬→𝜑¬𝜓𝜓	Modus ponens 655, 656	simprim
658	→¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓] into id
659	→→¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
660	→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 658, 659
661	→¬¬¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓] into notnotr
662	→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
663	→→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
664	→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Modus ponens 662, 663
665	→→¬¬¬→𝜑𝜓→¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬𝜑¬→𝜑𝜓] into ax-2
666	→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Modus ponens 664, 665
667	→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Modus ponens 661, 666
668	→→¬𝜑→¬→𝜑𝜓¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
669	→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Modus ponens 660, 668
670	→→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Subs [𝜑↗→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
671	→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Modus ponens 669, 670
672	→→¬¬¬→𝜑𝜓→→¬𝜑¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗→¬𝜑¬→𝜑𝜓, 𝜒↗→¬𝜑¬→𝜑𝜓] into ax-2
673	→→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓	Modus ponens 671, 672
674	→¬𝜑→¬¬¬→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
675	→→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
676	→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑	Modus ponens 674, 675
677	→→¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑𝜓¬𝜑] into ax-2
678	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬𝜑	Modus ponens 676, 677
679	→→¬¬¬→𝜑𝜓→¬𝜑¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬→𝜑𝜓] into ax-2
680	→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 667, 679
681	→→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
682	→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 680, 681
683	→→¬𝜑→→¬¬¬→𝜑𝜓¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑𝜓¬𝜑, 𝜒↗→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-2
684	→→¬𝜑→¬¬¬→𝜑𝜓¬𝜑→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 682, 683
685	→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 674, 684
686	→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-3
687	→→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬𝜑] into ax-1
688	→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 686, 687
689	→→¬𝜑→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬¬→𝜑𝜓] into ax-2
690	→→¬𝜑→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 688, 689
691	→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 685, 690
692	→→¬𝜑→→𝜑𝜓¬¬→𝜑𝜓→→¬𝜑→𝜑𝜓→¬𝜑¬¬→𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
693	→→¬𝜑→𝜑𝜓→¬𝜑¬¬→𝜑𝜓	Modus ponens 691, 692
694	→¬𝜑¬¬→𝜑𝜓	Modus ponens pm2.21, 693
695	→→¬𝜑¬¬→𝜑𝜓→¬→𝜑𝜓𝜑	Subs [𝜓↗¬→𝜑𝜓] into ax-3
696	→¬→𝜑𝜓𝜑	Modus ponens 694, 695	simplim
697	→𝜑→¬𝜒𝜑	Subs [𝜓↗¬𝜒] into ax-1
698	→→𝜑→¬𝜒𝜑→¬→𝜑𝜓→𝜑→¬𝜒𝜑	Subs [𝜑↗→𝜑→¬𝜒𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
699	→¬→𝜑𝜓→𝜑→¬𝜒𝜑	Modus ponens 697, 698
700	→→¬→𝜑𝜓→𝜑→¬𝜒𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→¬𝜒𝜑	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗→¬𝜒𝜑] into ax-2
701	→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→¬𝜒𝜑	Modus ponens 699, 700
702	→¬→𝜑𝜓→¬𝜒𝜑	Modus ponens simplim, 701
703	→→𝜑¬¬𝜑→¬𝜒→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬𝜒] into ax-1
704	→¬𝜒→𝜑¬¬𝜑	Modus ponens notnot, 703
705	→→¬𝜒→𝜑¬¬𝜑→→¬𝜒𝜑→¬𝜒¬¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
706	→→¬𝜒𝜑→¬𝜒¬¬𝜑	Modus ponens 704, 705
707	→→→¬𝜒𝜑→¬𝜒¬¬𝜑→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑	Subs [𝜑↗→→¬𝜒𝜑→¬𝜒¬¬𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
708	→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑	Modus ponens 706, 707
709	→→¬→𝜑𝜓→→¬𝜒𝜑→¬𝜒¬¬𝜑→→¬→𝜑𝜓→¬𝜒𝜑→¬→𝜑𝜓→¬𝜒¬¬𝜑	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒𝜑, 𝜒↗→¬𝜒¬¬𝜑] into ax-2
710	→→¬→𝜑𝜓→¬𝜒𝜑→¬→𝜑𝜓→¬𝜒¬¬𝜑	Modus ponens 708, 709
711	→¬→𝜑𝜓→¬𝜒¬¬𝜑	Modus ponens 702, 710
712	→→¬𝜒¬¬𝜑→¬𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗¬𝜑] into ax-3
713	→→→¬𝜒¬¬𝜑→¬𝜑𝜒→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒	Subs [𝜑↗→→¬𝜒¬¬𝜑→¬𝜑𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
714	→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒	Modus ponens 712, 713
715	→→¬→𝜑𝜓→→¬𝜒¬¬𝜑→¬𝜑𝜒→→¬→𝜑𝜓→¬𝜒¬¬𝜑→¬→𝜑𝜓→¬𝜑𝜒	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒¬¬𝜑, 𝜒↗→¬𝜑𝜒] into ax-2
716	→→¬→𝜑𝜓→¬𝜒¬¬𝜑→¬→𝜑𝜓→¬𝜑𝜒	Modus ponens 714, 715
717	→¬→𝜑𝜓→¬𝜑𝜒	Modus ponens 711, 716	pm2.5g
718	→¬→𝜑𝜓→¬𝜑𝜓	Subs [𝜒↗𝜓] into pm2.5g	pm2.5
719	→→¬→𝜑𝜓¬→𝜑𝜓→𝜓→¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓¬→𝜑𝜓] into ax-1
720	→𝜓→¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 658, 719
721	→¬→𝜑𝜓→𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓] into ax-1
722	→→¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓→𝜓¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
723	→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓	Modus ponens 721, 722
724	→→¬¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→𝜓¬→𝜑𝜓] into ax-2
725	→→¬¬¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓	Modus ponens 723, 724
726	→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓	Modus ponens 661, 725
727	→→𝜓→¬→𝜑𝜓¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
728	→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓	Modus ponens 720, 727
729	→→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓	Subs [𝜑↗→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
730	→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓	Modus ponens 728, 729
731	→→¬¬¬→𝜑𝜓→→𝜓¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜓↗→𝜓¬→𝜑𝜓, 𝜒↗→𝜓¬→𝜑𝜓] into ax-2
732	→→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓	Modus ponens 730, 731
733	→𝜓→¬¬¬→𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗¬¬¬→𝜑𝜓] into ax-1
734	→→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓	Subs [𝜑↗→𝜓→¬¬¬→𝜑𝜓𝜓] into ax-1
735	→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓	Modus ponens 733, 734
736	→→𝜓→𝜓→¬¬¬→𝜑𝜓𝜓→→𝜓𝜓→𝜓→¬¬¬→𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜒↗→¬¬¬→𝜑𝜓𝜓] into ax-2
737	→→𝜓𝜓→𝜓→¬¬¬→𝜑𝜓𝜓	Modus ponens 735, 736
738	→→¬¬¬→𝜑𝜓→𝜓¬→𝜑𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
739	→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 726, 738
740	→→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-1
741	→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 739, 740
742	→→𝜓→→¬¬¬→𝜑𝜓𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→¬¬¬→𝜑𝜓𝜓, 𝜒↗→¬¬¬→𝜑𝜓¬→𝜑𝜓] into ax-2
743	→→𝜓→¬¬¬→𝜑𝜓𝜓→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 741, 742
744	→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 733, 743
745	→→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓] into ax-1
746	→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 686, 745
747	→→𝜓→→¬¬¬→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→¬¬¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬¬→𝜑𝜓] into ax-2
748	→→𝜓→¬¬¬→𝜑𝜓¬→𝜑𝜓→𝜓→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 746, 747
749	→𝜓→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 744, 748
750	→→𝜓→→𝜑𝜓¬¬→𝜑𝜓→→𝜓→𝜑𝜓→𝜓¬¬→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
751	→→𝜓→𝜑𝜓→𝜓¬¬→𝜑𝜓	Modus ponens 749, 750
752	→𝜓¬¬→𝜑𝜓	Modus ponens 208, 751
753	→→𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓	Subs [𝜑↗→𝜓¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
754	→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓	Modus ponens 752, 753
755	→𝜓→¬→𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
756	→→𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓	Subs [𝜑↗→𝜓→¬→𝜑𝜓𝜓, 𝜓↗¬¬𝜓] into ax-1
757	→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓	Modus ponens 755, 756
758	→→¬¬𝜓→𝜓→¬→𝜑𝜓𝜓→→¬¬𝜓𝜓→¬¬𝜓→¬→𝜑𝜓𝜓	Subs [𝜑↗¬¬𝜓, 𝜒↗→¬→𝜑𝜓𝜓] into ax-2
759	→→¬¬𝜓𝜓→¬¬𝜓→¬→𝜑𝜓𝜓	Modus ponens 757, 758
760	→¬¬𝜓→¬→𝜑𝜓𝜓	Modus ponens 570, 759
761	→→¬→𝜑𝜓→𝜓¬¬→𝜑𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
762	→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 754, 761
763	→→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
764	→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 762, 763
765	→→¬¬𝜓→→¬→𝜑𝜓𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗→¬→𝜑𝜓𝜓, 𝜒↗→¬→𝜑𝜓¬¬→𝜑𝜓] into ax-2
766	→→¬¬𝜓→¬→𝜑𝜓𝜓→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 764, 765
767	→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 760, 766
768	→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
769	→→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
770	→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓	Modus ponens 768, 769
771	→→¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬𝜓¬→𝜑𝜓] into ax-2
772	→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓	Modus ponens 770, 771
773	→→¬¬𝜓→¬→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
774	→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓	Modus ponens 767, 773
775	→→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓	Subs [𝜑↗→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
776	→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓	Modus ponens 774, 775
777	→→¬→𝜑𝜓→→¬¬𝜓¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬𝜓¬→𝜑𝜓, 𝜒↗→¬¬𝜓¬¬→𝜑𝜓] into ax-2
778	→→¬→𝜑𝜓→¬¬𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓	Modus ponens 776, 777
779	→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓	Modus ponens 768, 778
780	→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-3
781	→→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
782	→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Modus ponens 780, 781
783	→→¬→𝜑𝜓→→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬𝜓¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬𝜓] into ax-2
784	→→¬→𝜑𝜓→¬¬𝜓¬¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Modus ponens 782, 783
785	→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Modus ponens 779, 784
786	→→¬→𝜑𝜓→¬→𝜑𝜓¬𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬𝜓] into ax-2
787	→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓¬𝜓	Modus ponens 785, 786
788	→¬→𝜑𝜓¬𝜓	Modus ponens 658, 787	conax1
789	→¬𝜓→𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗𝜒] into ax-1
790	→→¬𝜓→𝜒¬𝜓→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓	Subs [𝜑↗→¬𝜓→𝜒¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
791	→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓	Modus ponens 789, 790
792	→→¬→𝜑𝜓→¬𝜓→𝜒¬𝜓→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→𝜒¬𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜒¬𝜓] into ax-2
793	→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→𝜒¬𝜓	Modus ponens 791, 792
794	→¬→𝜑𝜓→𝜒¬𝜓	Modus ponens conax1, 793	conax1k
795	→¬→𝜑𝜓→𝜑¬𝜓	Subs [𝜒↗𝜑] into conax1k	pm2.51
796	→¬→𝜑𝜓→¬𝜑¬𝜓	Subs [𝜒↗¬𝜑] into conax1k	pm2.52
797	→¬𝜓→¬𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜒] into ax-1
798	→→¬𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓	Subs [𝜑↗→¬𝜓→¬𝜒¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
799	→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓	Modus ponens 797, 798
800	→→¬→𝜑𝜓→¬𝜓→¬𝜒¬𝜓→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→¬𝜒¬𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗→¬𝜒¬𝜓] into ax-2
801	→→¬→𝜑𝜓¬𝜓→¬→𝜑𝜓→¬𝜒¬𝜓	Modus ponens 799, 800
802	→¬→𝜑𝜓→¬𝜒¬𝜓	Modus ponens conax1, 801
803	→→¬𝜒¬𝜓→𝜓𝜒	Subs [𝜑↗𝜒] into ax-3
804	→→→¬𝜒¬𝜓→𝜓𝜒→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒	Subs [𝜑↗→→¬𝜒¬𝜓→𝜓𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
805	→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒	Modus ponens 803, 804
806	→→¬→𝜑𝜓→→¬𝜒¬𝜓→𝜓𝜒→→¬→𝜑𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→𝜓𝜒	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬𝜒¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
807	→→¬→𝜑𝜓→¬𝜒¬𝜓→¬→𝜑𝜓→𝜓𝜒	Modus ponens 805, 806
808	→¬→𝜑𝜓→𝜓𝜒	Modus ponens 802, 807	pm2.521g
809	→→𝜑→𝜒𝜑→¬→𝜑𝜓→𝜑→𝜒𝜑	Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
810	→¬→𝜑𝜓→𝜑→𝜒𝜑	Modus ponens 13, 809
811	→→¬→𝜑𝜓→𝜑→𝜒𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→𝜒𝜑	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2
812	→→¬→𝜑𝜓𝜑→¬→𝜑𝜓→𝜒𝜑	Modus ponens 810, 811
813	→¬→𝜑𝜓→𝜒𝜑	Modus ponens simplim, 812	pm2.521g2
814	→¬→𝜑𝜓→𝜓𝜑	Subs [𝜒↗𝜑] into pm2.521g	pm2.521
815	→𝜑→𝜒𝜒	Subs [𝜓↗𝜒] into idd
816	→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒	Subs [𝜑↗→𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
817	→→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1
818	→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒	Modus ponens 816, 817
819	→→𝜑→→𝜒𝜒→¬→𝜑¬𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→¬→𝜑¬𝜓→𝜒𝜒	Subs [𝜓↗→𝜒𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜒𝜒] into ax-2
820	→→𝜑→𝜒𝜒→𝜑→¬→𝜑¬𝜓→𝜒𝜒	Modus ponens 818, 819
821	→𝜑→¬→𝜑¬𝜓→𝜒𝜒	Modus ponens 815, 820
822	→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜒] into ax-2
823	→→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒, 𝜓↗𝜑] into ax-1
824	→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒	Modus ponens 822, 823
825	→→𝜑→→¬→𝜑¬𝜓→𝜒𝜒→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒	Subs [𝜓↗→¬→𝜑¬𝜓→𝜒𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒] into ax-2
826	→→𝜑→¬→𝜑¬𝜓→𝜒𝜒→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒	Modus ponens 824, 825
827	→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒	Modus ponens 821, 826
828	→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓	Subs [𝜑↗→𝜓¬→𝜑¬𝜓, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
829	→→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓, 𝜓↗𝜑] into ax-1
830	→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓	Modus ponens 828, 829
831	→→𝜑→→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓	Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓] into ax-2
832	→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓	Modus ponens 830, 831
833	→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓	Modus ponens pm3.2im, 832
834	→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
835	→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜑↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
836	→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 834, 835
837	→→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→→𝜓¬→𝜑¬𝜓→𝜓𝜒] into ax-2
838	→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 836, 837
839	→→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜑↗→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗𝜑] into ax-1
840	→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 838, 839
841	→→𝜑→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒] into ax-2
842	→→𝜑→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 840, 841
843	→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 827, 842
844	→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
845	→→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
846	→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Modus ponens 844, 845
847	→→𝜑→→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒, 𝜒↗→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒] into ax-2
848	→→𝜑→→¬→𝜑¬𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓𝜒→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Modus ponens 846, 847
849	→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Modus ponens 843, 848
850	→→𝜑→→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Subs [𝜓↗→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓, 𝜒↗→→¬→𝜑¬𝜓𝜒→𝜓𝜒] into ax-2
851	→→𝜑→→¬→𝜑¬𝜓𝜒→𝜓¬→𝜑¬𝜓→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Modus ponens 849, 850
852	→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒	Modus ponens 833, 851
853	→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓𝜒] into id
854	→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗𝜑] into ax-1
855	→→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
856	→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒	Modus ponens 854, 855
857	→→→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜑→¬→𝜑¬𝜓𝜒] into ax-2
858	→→→¬→𝜑¬𝜓𝜒→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒	Modus ponens 856, 857
859	→→𝜑→→¬→𝜑¬𝜓𝜒→𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜓↗→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
860	→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 852, 859
861	→→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜒] into ax-1
862	→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 860, 861
863	→→→¬→𝜑¬𝜓𝜒→→𝜑→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒→→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜑→¬→𝜑¬𝜓𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
864	→→→¬→𝜑¬𝜓𝜒→𝜑→¬→𝜑¬𝜓𝜒→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 862, 863
865	→→¬→𝜑¬𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 854, 864	expt
866	→¬→𝜑¬𝜓𝜑	Subs [𝜓↗¬𝜓] into simplim
867	→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→𝜓𝜒] into id
868	→→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
869	→𝜑→→𝜓𝜒→𝜓𝜒	Modus ponens 867, 868
870	→→𝜑→→𝜓𝜒→𝜓𝜒→→𝜑→𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
871	→𝜑→→𝜑→𝜓𝜒𝜑	Subs [𝜓↗→𝜑→𝜓𝜒] into ax-1
872	→→𝜑→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑	Subs [𝜑↗→𝜑→→𝜑→𝜓𝜒𝜑, 𝜓↗¬→𝜑¬𝜓] into ax-1
873	→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑	Modus ponens 871, 872
874	→→¬→𝜑¬𝜓→𝜑→→𝜑→𝜓𝜒𝜑→→¬→𝜑¬𝜓𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜑] into ax-2
875	→→¬→𝜑¬𝜓𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑	Modus ponens 873, 874
876	→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑	Modus ponens 866, 875
877	→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜓𝜒] into ax-2
878	→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒	Modus ponens 139, 877
879	→→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
880	→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒	Modus ponens 878, 879
881	→→¬→𝜑¬𝜓→→→𝜑→𝜓𝜒𝜑→→𝜑→𝜓𝜒→𝜓𝜒→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜑, 𝜒↗→→𝜑→𝜓𝜒→𝜓𝜒] into ax-2
882	→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜑→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒	Modus ponens 880, 881
883	→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒	Modus ponens 876, 882
884	→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
885	→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
886	→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒	Modus ponens 884, 885
887	→→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜑→𝜓𝜒] into ax-2
888	→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒	Modus ponens 886, 887
889	→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
890	→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 883, 889
891	→→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜑↗→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
892	→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 890, 891
893	→→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓→𝜑→𝜓𝜒, 𝜒↗→¬→𝜑¬𝜓→𝜓𝜒] into ax-2
894	→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 892, 893
895	→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒	Modus ponens 884, 894
896	→→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓	Subs [𝜑↗→¬→𝜑¬𝜓𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1
897	→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓	Modus ponens simprim, 896
898	→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒	Subs [𝜑↗¬→𝜑¬𝜓] into ax-2
899	→→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
900	→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒	Modus ponens 898, 899
901	→→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓→𝜓𝜒, 𝜒↗→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒] into ax-2
902	→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓→𝜓𝜒→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒	Modus ponens 900, 901
903	→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒	Modus ponens 895, 902
904	→→→𝜑→𝜓𝜒→→¬→𝜑¬𝜓𝜓→¬→𝜑¬𝜓𝜒→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→¬→𝜑¬𝜓𝜓, 𝜒↗→¬→𝜑¬𝜓𝜒] into ax-2
905	→→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜓→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒	Modus ponens 903, 904
906	→→𝜑→𝜓𝜒→¬→𝜑¬𝜓𝜒	Modus ponens 897, 905	impt
907	→→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬𝜑	Subs [𝜑↗→¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
908	→→𝜑¬𝜑→¬𝜑¬𝜑	Modus ponens 310, 907
909	→¬𝜑¬¬¬𝜑	Subs [𝜑↗¬𝜑] into notnot
910	→→¬𝜑¬¬¬𝜑→¬𝜑→¬𝜑¬¬¬𝜑	Subs [𝜑↗→¬𝜑¬¬¬𝜑, 𝜓↗¬𝜑] into ax-1
911	→¬𝜑→¬𝜑¬¬¬𝜑	Modus ponens 909, 910
912	→→¬𝜑→¬𝜑¬¬¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗¬¬¬𝜑] into ax-2
913	→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑	Modus ponens 911, 912
914	→→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑	Subs [𝜑↗→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
915	→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑	Modus ponens 913, 914
916	→→→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑¬¬¬𝜑→→→𝜑¬𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬¬¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬𝜑¬𝜑, 𝜒↗→¬𝜑¬¬¬𝜑] into ax-2
917	→→→𝜑¬𝜑→¬𝜑¬𝜑→→𝜑¬𝜑→¬𝜑¬¬¬𝜑	Modus ponens 915, 916
918	→→𝜑¬𝜑→¬𝜑¬¬¬𝜑	Modus ponens 908, 917
919	→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑	Subs [𝜓↗¬¬𝜑] into ax-3
920	→→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑	Subs [𝜑↗→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
921	→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑	Modus ponens 919, 920
922	→→→𝜑¬𝜑→→¬𝜑¬¬¬𝜑→¬¬𝜑𝜑→→→𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→¬¬𝜑𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬𝜑¬¬¬𝜑, 𝜒↗→¬¬𝜑𝜑] into ax-2
923	→→→𝜑¬𝜑→¬𝜑¬¬¬𝜑→→𝜑¬𝜑→¬¬𝜑𝜑	Modus ponens 921, 922
924	→→𝜑¬𝜑→¬¬𝜑𝜑	Modus ponens 918, 923
925	→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗¬¬𝜑] into ax-1
926	→→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑	Subs [𝜑↗→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
927	→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑	Modus ponens 925, 926
928	→→→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→¬¬𝜑→𝜑¬𝜑] into ax-2
929	→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑	Modus ponens 927, 928
930	→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗¬𝜑] into ax-2
931	→→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑	Subs [𝜑↗→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
932	→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑	Modus ponens 930, 931
933	→→→𝜑¬𝜑→→¬¬𝜑→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑→𝜑¬𝜑, 𝜒↗→→¬¬𝜑𝜑→¬¬𝜑¬𝜑] into ax-2
934	→→→𝜑¬𝜑→¬¬𝜑→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑	Modus ponens 932, 933
935	→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑	Modus ponens 925, 934
936	→→→𝜑¬𝜑→→¬¬𝜑𝜑→¬¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→¬¬𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑𝜑, 𝜒↗→¬¬𝜑¬𝜑] into ax-2
937	→→→𝜑¬𝜑→¬¬𝜑𝜑→→𝜑¬𝜑→¬¬𝜑¬𝜑	Modus ponens 935, 936
938	→→𝜑¬𝜑→¬¬𝜑¬𝜑	Modus ponens 924, 937
939	→¬¬𝜑→¬𝜑¬→𝜑¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜑] into pm2.21
940	→→¬¬𝜑→¬𝜑¬→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜑] into ax-2
941	→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑	Modus ponens 939, 940
942	→→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑	Subs [𝜑↗→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
943	→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑	Modus ponens 941, 942
944	→→→𝜑¬𝜑→→¬¬𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑¬𝜑, 𝜒↗→¬¬𝜑¬→𝜑¬𝜑] into ax-2
945	→→→𝜑¬𝜑→¬¬𝜑¬𝜑→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑	Modus ponens 943, 944
946	→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑	Modus ponens 938, 945
947	→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-3
948	→→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Subs [𝜑↗→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑, 𝜓↗→𝜑¬𝜑] into ax-1
949	→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Modus ponens 947, 948
950	→→→𝜑¬𝜑→→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→¬¬𝜑¬→𝜑¬𝜑, 𝜒↗→→𝜑¬𝜑¬𝜑] into ax-2
951	→→→𝜑¬𝜑→¬¬𝜑¬→𝜑¬𝜑→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Modus ponens 949, 950
952	→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Modus ponens 946, 951
953	→→→𝜑¬𝜑→→𝜑¬𝜑¬𝜑→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗¬𝜑] into ax-2
954	→→→𝜑¬𝜑→𝜑¬𝜑→→𝜑¬𝜑¬𝜑	Modus ponens 952, 953
955	→→𝜑¬𝜑¬𝜑	Modus ponens 421, 954	pm2.01
956	→→¬𝜑𝜓→𝜓𝜓	Subs [𝜑↗→¬𝜑𝜓] into idd
957	→¬𝜑→→¬𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜑𝜓] into ax-1
958	→→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑	Subs [𝜑↗→¬𝜑→→¬𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
959	→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑	Modus ponens 957, 958
960	→→¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→→¬𝜑𝜓¬𝜑] into ax-2
961	→→¬𝜑¬𝜑→¬𝜑→→¬𝜑𝜓¬𝜑	Modus ponens 959, 960
962	→→→¬𝜑𝜓→¬𝜑𝜓→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into ax-2
963	→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓	Modus ponens 447, 962
964	→→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓	Subs [𝜑↗→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓, 𝜓↗¬𝜑] into ax-1
965	→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓	Modus ponens 963, 964
966	→→¬𝜑→→→¬𝜑𝜓¬𝜑→→¬𝜑𝜓𝜓→→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→→¬𝜑𝜓𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→→¬𝜑𝜓¬𝜑, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
967	→→¬𝜑→→¬𝜑𝜓¬𝜑→¬𝜑→→¬𝜑𝜓𝜓	Modus ponens 965, 966
968	→¬𝜑→→¬𝜑𝜓𝜓	Modus ponens 957, 967
969	→𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
970	→→𝜓→→¬𝜑𝜓𝜓→𝜓→𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜓→→¬𝜑𝜓𝜓] into ax-1
971	→𝜓→𝜓→→¬𝜑𝜓𝜓	Modus ponens 969, 970
972	→→𝜓→𝜓→→¬𝜑𝜓𝜓→→𝜓𝜓→𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
973	→→𝜓𝜓→𝜓→→¬𝜑𝜓𝜓	Modus ponens 971, 972
974	→→→¬𝜑𝜓→𝜓𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→¬𝜑𝜓, 𝜒↗𝜓] into ax-2
975	→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Modus ponens 956, 974
976	→→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-1
977	→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Modus ponens 975, 976
978	→→𝜓→→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜓→→¬𝜑𝜓𝜓→𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
979	→→𝜓→→¬𝜑𝜓𝜓→𝜓→→¬𝜑𝜓𝜓	Modus ponens 977, 978
980	→→𝜓→→¬𝜑𝜓𝜓→𝜑→𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜓→→¬𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
981	→𝜑→𝜓→→¬𝜑𝜓𝜓	Modus ponens 969, 980
982	→→𝜑→𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓	Subs [𝜒↗→→¬𝜑𝜓𝜓] into ax-2
983	→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓	Modus ponens 981, 982
984	→→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓	Subs [𝜑↗→¬𝜑→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
985	→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓	Modus ponens 968, 984
986	→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓	Subs [𝜑↗→→¬𝜑𝜓𝜓] into notnot
987	→→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓	Subs [𝜑↗→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓, 𝜓↗¬𝜑] into ax-1
988	→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓	Modus ponens 986, 987
989	→→¬𝜑→→→¬𝜑𝜓𝜓¬¬→→¬𝜑𝜓𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗¬¬→→¬𝜑𝜓𝜓] into ax-2
990	→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓	Modus ponens 988, 989
991	→→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓	Subs [𝜑↗→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
992	→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓	Modus ponens 990, 991
993	→→→𝜑𝜓→→¬𝜑→→¬𝜑𝜓𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑→→¬𝜑𝜓𝜓, 𝜒↗→¬𝜑¬¬→→¬𝜑𝜓𝜓] into ax-2
994	→→→𝜑𝜓→¬𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓	Modus ponens 992, 993
995	→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓	Modus ponens 985, 994
996	→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑	Subs [𝜓↗¬→→¬𝜑𝜓𝜓] into ax-3
997	→→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑	Subs [𝜑↗→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
998	→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑	Modus ponens 996, 997
999	→→→𝜑𝜓→→¬𝜑¬¬→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓𝜑→→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑¬¬→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓𝜑] into ax-2
1000	→→→𝜑𝜓→¬𝜑¬¬→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑	Modus ponens 998, 999
1001	→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑	Modus ponens 995, 1000
1002	→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑→→¬𝜑𝜓𝜓, 𝜓↗¬→→¬𝜑𝜓𝜓] into ax-1
1003	→→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓	Subs [𝜑↗→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1004	→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓	Modus ponens 1002, 1003
1005	→→→𝜑𝜓→→𝜑→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓] into ax-2
1006	→→→𝜑𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓	Modus ponens 1004, 1005
1007	→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓	Modus ponens 983, 1006
1008	→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗¬→→¬𝜑𝜓𝜓, 𝜓↗𝜑, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
1009	→→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1010	→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Modus ponens 1008, 1009
1011	→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓, 𝜒↗→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-2
1012	→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→𝜑→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Modus ponens 1010, 1011
1013	→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Modus ponens 1007, 1012
1014	→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓𝜑→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓𝜑, 𝜒↗→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓] into ax-2
1015	→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓𝜑→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Modus ponens 1013, 1014
1016	→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓	Modus ponens 1001, 1015
1017	→¬→→¬𝜑𝜓𝜓→→→¬𝜑𝜓𝜓¬→𝜑𝜓	Subs [𝜑↗→→¬𝜑𝜓𝜓, 𝜓↗¬→𝜑𝜓] into pm2.21
1018	→→¬→→¬𝜑𝜓𝜓→→→¬𝜑𝜓𝜓¬→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓	Subs [𝜑↗¬→→¬𝜑𝜓𝜓, 𝜓↗→→¬𝜑𝜓𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
1019	→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓	Modus ponens 1017, 1018
1020	→→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓	Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1021	→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓	Modus ponens 1019, 1020
1022	→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓, 𝜒↗→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓] into ax-2
1023	→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓	Modus ponens 1021, 1022
1024	→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓	Modus ponens 1016, 1023
1025	→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-3
1026	→→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1027	→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens 1025, 1026
1028	→→→𝜑𝜓→→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→→¬𝜑𝜓𝜓] into ax-2
1029	→→→𝜑𝜓→¬→→¬𝜑𝜓𝜓¬→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens 1027, 1028
1030	→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens 1024, 1029
1031	→→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
1032	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens 1030, 1031
1033	→→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens 24, 1032	pm2.61
1034	→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1035	→→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓	Subs [𝜑↗→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
1036	→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓	Modus ponens 1034, 1035
1037	→→→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗→→𝜑𝜓→¬𝜑𝜓] into ax-2
1038	→→→¬𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓	Modus ponens 1036, 1037
1039	→→→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑𝜓, 𝜒↗𝜓] into ax-2
1040	→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓	Modus ponens pm2.61, 1039
1041	→→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓	Subs [𝜑↗→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
1042	→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓	Modus ponens 1040, 1041
1043	→→→¬𝜑𝜓→→→𝜑𝜓→¬𝜑𝜓→→𝜑𝜓𝜓→→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓𝜓	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→→𝜑𝜓→¬𝜑𝜓, 𝜒↗→→𝜑𝜓𝜓] into ax-2
1044	→→→¬𝜑𝜓→→𝜑𝜓→¬𝜑𝜓→→¬𝜑𝜓→→𝜑𝜓𝜓	Modus ponens 1042, 1043
1045	→→¬𝜑𝜓→→𝜑𝜓𝜓	Modus ponens 1034, 1044	pm2.6
1046	→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜑𝜓] into ax-1
1047	→→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1048	→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓	Modus ponens 1046, 1047
1049	→→→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→¬𝜑𝜓→𝜑𝜓] into ax-2
1050	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓	Modus ponens 1048, 1049
1051	→→→¬𝜑𝜓→→𝜑𝜓𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
1052	→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens pm2.6, 1051
1053	→→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓, 𝜓↗→𝜑𝜓] into ax-1
1054	→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens 1052, 1053
1055	→→→𝜑𝜓→→→¬𝜑𝜓→𝜑𝜓→→¬𝜑𝜓𝜓→→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→¬𝜑𝜓→𝜑𝜓, 𝜒↗→→¬𝜑𝜓𝜓] into ax-2
1056	→→→𝜑𝜓→→¬𝜑𝜓→𝜑𝜓→→𝜑𝜓→→¬𝜑𝜓𝜓	Modus ponens 1054, 1055
1057	→→𝜑𝜓→¬𝜑¬𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑] into idd
1058	→¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓] into ax-1
1059	→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
1060	→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1058, 1059
1061	→→¬𝜑→¬𝜑→→𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1062	→→¬𝜑¬𝜑→¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1060, 1061
1063	→→→𝜑𝜓→¬𝜑¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜑] into ax-2
1064	→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1057, 1063
1065	→→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
1066	→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1064, 1065
1067	→→¬𝜑→→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1068	→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1066, 1067
1069	→¬𝜓→→𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→𝜑𝜓] into ax-1
1070	→→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓	Subs [𝜑↗→¬𝜓→→𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
1071	→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓	Modus ponens 1069, 1070
1072	→→¬𝜓→¬𝜓→→𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→→𝜑𝜓¬𝜓] into ax-2
1073	→→¬𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜓	Modus ponens 1071, 1072
1074	→→→𝜑𝜓→¬𝜓¬𝜑→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
1075	→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑	Modus ponens con3, 1074
1076	→→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
1077	→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1075, 1076
1078	→→¬𝜓→→→𝜑𝜓¬𝜓→→𝜑𝜓¬𝜑→→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→→𝜑𝜓¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1079	→→¬𝜓→→𝜑𝜓¬𝜓→¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1077, 1078
1080	→¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1069, 1079
1081	→→¬𝜓→→𝜑𝜓¬𝜑→𝜑→¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗→¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗𝜑] into ax-1
1082	→𝜑→¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1080, 1081
1083	→→𝜑→¬𝜓→→𝜑𝜓¬𝜑→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑	Subs [𝜓↗¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1084	→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑	Modus ponens 1082, 1083
1085	→→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1086	→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1058, 1085
1087	→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑	Subs [𝜑↗→→𝜑𝜓¬𝜑] into notnot
1088	→→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑	Subs [𝜑↗→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
1089	→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑	Modus ponens 1087, 1088
1090	→→¬𝜑→→→𝜑𝜓¬𝜑¬¬→→𝜑𝜓¬𝜑→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗¬¬→→𝜑𝜓¬𝜑] into ax-2
1091	→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑	Modus ponens 1089, 1090
1092	→→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑	Subs [𝜑↗→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1093	→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑	Modus ponens 1091, 1092
1094	→→→𝜑¬𝜓→→¬𝜑→→𝜑𝜓¬𝜑→¬𝜑¬¬→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬𝜑¬¬→→𝜑𝜓¬𝜑] into ax-2
1095	→→→𝜑¬𝜓→¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑	Modus ponens 1093, 1094
1096	→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑	Modus ponens 1086, 1095
1097	→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑	Subs [𝜓↗¬→→𝜑𝜓¬𝜑] into ax-3
1098	→→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑	Subs [𝜑↗→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1099	→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑	Modus ponens 1097, 1098
1100	→→→𝜑¬𝜓→→¬𝜑¬¬→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑𝜑→→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬𝜑¬¬→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑𝜑] into ax-2
1101	→→→𝜑¬𝜓→¬𝜑¬¬→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑	Modus ponens 1099, 1100
1102	→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑	Modus ponens 1096, 1101
1103	→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑→→𝜑𝜓¬𝜑, 𝜓↗¬→→𝜑𝜓¬𝜑] into ax-1
1104	→→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1105	→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑	Modus ponens 1103, 1104
1106	→→→𝜑¬𝜓→→𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑] into ax-2
1107	→→→𝜑¬𝜓→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑	Modus ponens 1105, 1106
1108	→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑	Modus ponens 1084, 1107
1109	→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗¬→→𝜑𝜓¬𝜑, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1110	→→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1111	→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1109, 1110
1112	→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑, 𝜒↗→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑] into ax-2
1113	→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1111, 1112
1114	→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1108, 1113
1115	→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑𝜑→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑] into ax-2
1116	→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1114, 1115
1117	→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑	Modus ponens 1102, 1116
1118	→¬→→𝜑𝜓¬𝜑→→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗→→𝜑𝜓¬𝜑, 𝜓↗¬→𝜑¬𝜓] into pm2.21
1119	→→¬→→𝜑𝜓¬𝜑→→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬→→𝜑𝜓¬𝜑, 𝜓↗→→𝜑𝜓¬𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2
1120	→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Modus ponens 1118, 1119
1121	→→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
1122	→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Modus ponens 1120, 1121
1123	→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑, 𝜒↗→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓] into ax-2
1124	→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑→→𝜑𝜓¬𝜑→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Modus ponens 1122, 1123
1125	→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓	Modus ponens 1117, 1124
1126	→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-3
1127	→→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑, 𝜓↗→𝜑¬𝜓] into ax-1
1128	→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1126, 1127
1129	→→→𝜑¬𝜓→→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓→→𝜑𝜓¬𝜑] into ax-2
1130	→→→𝜑¬𝜓→¬→→𝜑𝜓¬𝜑¬→𝜑¬𝜓→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1128, 1129
1131	→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1125, 1130
1132	→→→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→→𝜑𝜓¬𝜑] into ax-2
1133	→→→𝜑¬𝜓→𝜑¬𝜓→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 1131, 1132
1134	→→𝜑¬𝜓→→𝜑𝜓¬𝜑	Modus ponens 379, 1133
1135	→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
1136	→→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1137	→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓	Modus ponens 1135, 1136
1138	→→→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑¬𝜓→𝜑𝜓] into ax-2
1139	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓	Modus ponens 1137, 1138
1140	→→→𝜑¬𝜓→→𝜑𝜓¬𝜑→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬𝜑] into ax-2
1141	→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑	Modus ponens 1134, 1140
1142	→→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑	Subs [𝜑↗→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑, 𝜓↗→𝜑𝜓] into ax-1
1143	→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑	Modus ponens 1141, 1142
1144	→→→𝜑𝜓→→→𝜑¬𝜓→𝜑𝜓→→𝜑¬𝜓¬𝜑→→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓¬𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑¬𝜓→𝜑𝜓, 𝜒↗→→𝜑¬𝜓¬𝜑] into ax-2
1145	→→→𝜑𝜓→→𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑¬𝜓¬𝜑	Modus ponens 1143, 1144
1146	→→𝜑𝜓→→𝜑¬𝜓¬𝜑	Modus ponens 1135, 1145	pm2.65
1147	→→𝜑𝜑→→𝜑𝜓→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜓] into ax-1
1148	→→𝜑𝜓→𝜑𝜑	Modus ponens id, 1147
1149	→→→𝜑𝜓→𝜑𝜑→→→𝜑𝜓𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
1150	→→→𝜑𝜓𝜑→→𝜑𝜓𝜑	Modus ponens 1148, 1149
1151	→→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑	Subs [𝜑↗→¬→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1152	→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑	Modus ponens simplim, 1151
1153	→→𝜑¬¬𝜑→¬→𝜑𝜓→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
1154	→¬→𝜑𝜓→𝜑¬¬𝜑	Modus ponens notnot, 1153
1155	→→¬→𝜑𝜓→𝜑¬¬𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
1156	→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑	Modus ponens 1154, 1155
1157	→→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑	Subs [𝜑↗→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1158	→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑	Modus ponens 1156, 1157
1159	→→→→𝜑𝜓𝜑→→¬→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬→𝜑𝜓𝜑, 𝜒↗→¬→𝜑𝜓¬¬𝜑] into ax-2
1160	→→→→𝜑𝜓𝜑→¬→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑	Modus ponens 1158, 1159
1161	→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑	Modus ponens 1152, 1160
1162	→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬𝜑] into ax-3
1163	→→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓	Subs [𝜑↗→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1164	→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓	Modus ponens 1162, 1163
1165	→→→→𝜑𝜓𝜑→→¬→𝜑𝜓¬¬𝜑→¬𝜑→𝜑𝜓→→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬→𝜑𝜓¬¬𝜑, 𝜒↗→¬𝜑→𝜑𝜓] into ax-2
1166	→→→→𝜑𝜓𝜑→¬→𝜑𝜓¬¬𝜑→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓	Modus ponens 1164, 1165
1167	→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓	Modus ponens 1161, 1166
1168	→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗¬𝜑] into ax-1
1169	→→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1170	→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑	Modus ponens 1168, 1169
1171	→→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→¬𝜑→→𝜑𝜓𝜑] into ax-2
1172	→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑	Modus ponens 1170, 1171
1173	→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓, 𝜒↗𝜑] into ax-2
1174	→→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑	Subs [𝜑↗→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1175	→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑	Modus ponens 1173, 1174
1176	→→→→𝜑𝜓𝜑→→¬𝜑→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑→→𝜑𝜓𝜑, 𝜒↗→→¬𝜑→𝜑𝜓→¬𝜑𝜑] into ax-2
1177	→→→→𝜑𝜓𝜑→¬𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑	Modus ponens 1175, 1176
1178	→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑	Modus ponens 1168, 1177
1179	→→→→𝜑𝜓𝜑→→¬𝜑→𝜑𝜓→¬𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→¬𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑→𝜑𝜓, 𝜒↗→¬𝜑𝜑] into ax-2
1180	→→→→𝜑𝜓𝜑→¬𝜑→𝜑𝜓→→→𝜑𝜓𝜑→¬𝜑𝜑	Modus ponens 1178, 1179
1181	→→→𝜑𝜓𝜑→¬𝜑𝜑	Modus ponens 1167, 1180
1182	→¬𝜑→𝜑¬→→𝜑𝜓𝜑	Subs [𝜓↗¬→→𝜑𝜓𝜑] into pm2.21
1183	→→¬𝜑→𝜑¬→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑	Subs [𝜑↗¬𝜑, 𝜓↗𝜑, 𝜒↗¬→→𝜑𝜓𝜑] into ax-2
1184	→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑	Modus ponens 1182, 1183
1185	→→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑	Subs [𝜑↗→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1186	→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑	Modus ponens 1184, 1185
1187	→→→→𝜑𝜓𝜑→→¬𝜑𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→→𝜑𝜓𝜑→¬𝜑𝜑→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑𝜑, 𝜒↗→¬𝜑¬→→𝜑𝜓𝜑] into ax-2
1188	→→→→𝜑𝜓𝜑→¬𝜑𝜑→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑	Modus ponens 1186, 1187
1189	→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑	Modus ponens 1181, 1188
1190	→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Subs [𝜓↗→→𝜑𝜓𝜑] into ax-3
1191	→→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜑] into ax-1
1192	→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Modus ponens 1190, 1191
1193	→→→→𝜑𝜓𝜑→→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→¬𝜑¬→→𝜑𝜓𝜑, 𝜒↗→→→𝜑𝜓𝜑𝜑] into ax-2
1194	→→→→𝜑𝜓𝜑→¬𝜑¬→→𝜑𝜓𝜑→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Modus ponens 1192, 1193
1195	→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Modus ponens 1189, 1194
1196	→→→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗𝜑] into ax-2
1197	→→→→𝜑𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜑𝜑	Modus ponens 1195, 1196
1198	→→→𝜑𝜓𝜑𝜑	Modus ponens 1150, 1197	peirce
1199	→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜒↗𝜑] into imim1
1200	→→→→𝜑𝜓𝜑𝜑→→𝜓𝜑→→→𝜑𝜓𝜑𝜑	Subs [𝜑↗→→→𝜑𝜓𝜑𝜑, 𝜓↗→𝜓𝜑] into ax-1
1201	→→𝜓𝜑→→→𝜑𝜓𝜑𝜑	Modus ponens peirce, 1200
1202	→→→𝜓𝜑→→→𝜑𝜓𝜑𝜑→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗𝜑] into ax-2
1203	→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑	Modus ponens 1201, 1202
1204	→→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑	Subs [𝜑↗→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑, 𝜓↗→→𝜑𝜓𝜓] into ax-1
1205	→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑	Modus ponens 1203, 1204
1206	→→→→𝜑𝜓𝜓→→→𝜓𝜑→→𝜑𝜓𝜑→→𝜓𝜑𝜑→→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜓→→𝜓𝜑𝜑	Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→→𝜓𝜑→→𝜑𝜓𝜑, 𝜒↗→→𝜓𝜑𝜑] into ax-2
1207	→→→→𝜑𝜓𝜓→→𝜓𝜑→→𝜑𝜓𝜑→→→𝜑𝜓𝜓→→𝜓𝜑𝜑	Modus ponens 1205, 1206
1208	→→→𝜑𝜓𝜓→→𝜓𝜑𝜑	Modus ponens 1199, 1207	looinv
1209	→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→𝜑𝜑] into pm2.01
1210	→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1211	→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Modus ponens id, 1210
1212	→→𝜑𝜑→𝜑𝜑	Subs [𝜑↗→𝜑𝜑] into id
1213	→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1214	→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1209, 1213
1215	→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑] into notnotr
1216	→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1217	→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1218	→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1216, 1217
1219	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2
1220	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1218, 1219
1221	→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1215, 1220
1222	→→→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1223	→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1214, 1222
1224	→→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1225	→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1223, 1224
1226	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬→𝜑𝜑] into ax-2
1227	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1225, 1226
1228	→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1229	→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1230	→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Modus ponens 1228, 1229
1231	→→→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑] into ax-2
1232	→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Modus ponens 1230, 1231
1233	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1234	→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1215, 1233
1235	→→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1236	→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1234, 1235
1237	→→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1238	→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1236, 1237
1239	→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1228, 1238
1240	→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-3
1241	→→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-1
1242	→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1240, 1241
1243	→→→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1244	→→→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1242, 1243
1245	→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1239, 1244
1246	→→→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1247	→→→𝜑𝜑→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1245, 1246
1248	→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1212, 1247
1249	→¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑] into id
1250	→→¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1251	→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1249, 1250
1252	→¬¬¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑] into notnotr
1253	→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1254	→→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1
1255	→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1253, 1254
1256	→→¬¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1257	→→¬¬¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1255, 1256
1258	→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1252, 1257
1259	→→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1260	→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1251, 1259
1261	→→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1
1262	→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1260, 1261
1263	→→¬¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1264	→→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1262, 1263
1265	→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑] into id
1266	→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬→𝜑𝜑] into ax-1
1267	→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1268	→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1266, 1267
1269	→→→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2
1270	→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1268, 1269
1271	→→¬¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬→𝜑𝜑] into ax-2
1272	→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1258, 1271
1273	→→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1274	→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1272, 1273
1275	→→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1276	→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1274, 1275
1277	→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1266, 1276
1278	→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗¬¬→𝜑𝜑, 𝜓↗→𝜑𝜑] into ax-3
1279	→→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑] into ax-1
1280	→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1278, 1279
1281	→→→→𝜑𝜑¬→𝜑𝜑→→¬¬¬→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬¬¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→→𝜑𝜑¬¬→𝜑𝜑] into ax-2
1282	→→→→𝜑𝜑¬→𝜑𝜑→¬¬¬→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1280, 1281
1283	→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1277, 1282
1284	→→→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬¬→𝜑𝜑→→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2
1285	→→→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1283, 1284
1286	→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1211, 1285
1287	→→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1288	→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1286, 1287
1289	→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1290	→→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1291	→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1289, 1290
1292	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑] into ax-2
1293	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1291, 1292
1294	→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1215, 1293
1295	→→¬→𝜑𝜑→→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2
1296	→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1288, 1295
1297	→→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1298	→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1296, 1297
1299	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→𝜑𝜑] into ax-2
1300	→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1298, 1299
1301	→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1294, 1300
1302	→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1303	→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1304	→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1302, 1303
1305	→→¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1306	→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1304, 1305
1307	→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬¬→𝜑𝜑] into ax-2
1308	→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1301, 1307
1309	→→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1310	→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1308, 1309
1311	→→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑] into ax-2
1312	→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1310, 1311
1313	→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑	Modus ponens 1302, 1312
1314	→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-3
1315	→→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1316	→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1314, 1315
1317	→→¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1318	→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1316, 1317
1319	→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1313, 1318
1320	→→¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1321	→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1319, 1320
1322	→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1249, 1321
1323	→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑] into id
1324	→→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1325	→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1323, 1324
1326	→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑] into notnotr
1327	→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1328	→→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1329	→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1327, 1328
1330	→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1331	→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1329, 1330
1332	→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1326, 1331
1333	→→¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1334	→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1325, 1333
1335	→→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1336	→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1334, 1335
1337	→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1338	→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1336, 1337
1339	→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1340	→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1341	→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1339, 1340
1342	→→¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑] into ax-2
1343	→→¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑	Modus ponens 1341, 1342
1344	→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑, 𝜒↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1345	→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1332, 1344
1346	→→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1347	→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1345, 1346
1348	→→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1349	→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1347, 1348
1350	→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1339, 1349
1351	→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-3
1352	→→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬→𝜑𝜑] into ax-1
1353	→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1351, 1352
1354	→→¬→𝜑𝜑→→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1355	→→¬→𝜑𝜑→¬¬¬¬→→𝜑𝜑¬→𝜑𝜑¬¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1353, 1354
1356	→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1350, 1355
1357	→→¬→𝜑𝜑→¬→→𝜑𝜑¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→𝜑𝜑, 𝜓↗¬→→𝜑𝜑¬→𝜑𝜑, 𝜒↗¬¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1358	→→¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1356, 1357
1359	→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1322, 1358
1360	→→¬→𝜑𝜑¬¬¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-3
1361	→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑	Modus ponens 1359, 1360
1362	→→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗¬¬→→𝜑𝜑¬→𝜑𝜑] into ax-1
1363	→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1248, 1362
1364	→→¬¬→→𝜑𝜑¬→𝜑𝜑→→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬¬→→𝜑𝜑¬→𝜑𝜑, 𝜓↗→𝜑𝜑, 𝜒↗¬→→𝜑𝜑¬→𝜑𝜑] into ax-2
1365	→→¬¬→→𝜑𝜑¬→𝜑𝜑→𝜑𝜑→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1363, 1364
1366	→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1361, 1365
1367	→→¬¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑¬→→𝜑𝜑¬→𝜑𝜑	Subs [𝜑↗¬→→𝜑𝜑¬→𝜑𝜑] into pm2.18
1368	¬→→𝜑𝜑¬→𝜑𝜑	Modus ponens 1366, 1367	bijust0
1369	¬→→¬→→𝜑𝜓¬→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑] into bijust0	bijust
1370	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into simprim
1371	→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens df-bi, 1370
1372	→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into pm3.2im
1373	→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1
1374	→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1371, 1373
1375	→→→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
1376	→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓	Modus ponens 1374, 1375
1377	→→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1378	→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓	Modus ponens 1376, 1377
1379	→→→𝜑𝜓→→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→𝜓𝜑↔𝜑𝜓] into ax-2
1380	→→→𝜑𝜓→→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Modus ponens 1378, 1379
1381	→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Modus ponens 1372, 1380	impbi
1382	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into impbi
1383	→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into notnotr
1384	→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1385	→→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1386	→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1384, 1385
1387	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1388	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1386, 1387
1389	→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1383, 1388
1390	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1391	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1382, 1390
1392	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1393	→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1391, 1392
1394	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1395	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1393, 1394
1396	→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1389, 1395
1397	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id
1398	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1399	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1400	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1398, 1399
1401	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1402	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1400, 1401
1403	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1404	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1396, 1403
1405	→→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1406	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1404, 1405
1407	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1408	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1406, 1407
1409	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1398, 1408
1410	→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnot
1411	→→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1412	→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1410, 1411
1413	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1414	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1412, 1413
1415	→→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1416	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1414, 1415
1417	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1418	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1416, 1417
1419	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1409, 1418
1420	→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1421	→→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1422	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1420, 1421
1423	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1424	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1422, 1423
1425	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1419, 1424
1426	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id
1427	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1428	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1429	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1427, 1428
1430	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1431	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1429, 1430
1432	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1433	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1425, 1432
1434	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1435	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1433, 1434
1436	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1437	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1435, 1436
1438	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1427, 1437
1439	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1440	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens df-bi, 1439
1441	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into id
1442	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1443	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1440, 1442
1444	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnotr
1445	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1446	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1447	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1445, 1446
1448	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1449	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1447, 1448
1450	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1444, 1449
1451	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1452	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1443, 1451
1453	→→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1454	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1452, 1453
1455	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1456	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1454, 1455
1457	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1450, 1456
1458	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1459	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1460	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1458, 1459
1461	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1462	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1460, 1461
1463	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1464	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1457, 1463
1465	→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1466	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1464, 1465
1467	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1468	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1466, 1467
1469	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1458, 1468
1470	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3
1471	→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1472	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1470, 1471
1473	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1474	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1472, 1473
1475	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1469, 1474
1476	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1477	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1475, 1476
1478	→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1441, 1477
1479	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into id
1480	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1481	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1479, 1480
1482	→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into notnotr
1483	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1484	→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1439, 1483
1485	→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1486	→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1484, 1485
1487	→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1482, 1486
1488	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1489	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1481, 1488
1490	→→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1491	→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1489, 1490
1492	→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1493	→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1491, 1492
1494	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1495	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1496	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1494, 1495
1497	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1498	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1496, 1497
1499	→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1500	→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1487, 1499
1501	→→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1502	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1500, 1501
1503	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1504	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1502, 1503
1505	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1494, 1504
1506	→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3
1507	→→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1508	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1506, 1507
1509	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1510	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1508, 1509
1511	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1505, 1510
1512	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1513	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1511, 1512
1514	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1438, 1513
1515	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1516	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1514, 1515
1517	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1518	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1519	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1517, 1518
1520	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1521	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1519, 1520
1522	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1444, 1521
1523	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1524	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1516, 1523
1525	→→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1526	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1524, 1525
1527	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1528	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1526, 1527
1529	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1522, 1528
1530	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1531	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1532	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1530, 1531
1533	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1534	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1532, 1533
1535	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1536	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1529, 1535
1537	→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1538	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1536, 1537
1539	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1540	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1538, 1539
1541	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1530, 1540
1542	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-3
1543	→→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1544	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1542, 1543
1545	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1546	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1544, 1545
1547	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1541, 1546
1548	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1549	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1547, 1548
1550	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1479, 1549
1551	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into id
1552	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1553	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1551, 1552
1554	→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into notnotr
1555	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1556	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1557	→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1555, 1556
1558	→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1559	→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1557, 1558
1560	→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1554, 1559
1561	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1562	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1553, 1561
1563	→→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1564	→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1562, 1563
1565	→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1566	→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1564, 1565
1567	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1568	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1569	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1567, 1568
1570	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-2
1571	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1569, 1570
1572	→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1573	→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1560, 1572
1574	→→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1575	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1573, 1574
1576	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1577	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1575, 1576
1578	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1567, 1577
1579	→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1580	→→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into ax-1
1581	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1579, 1580
1582	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1583	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1581, 1582
1584	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1578, 1583
1585	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1586	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1584, 1585
1587	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1550, 1586
1588	→→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1589	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1587, 1588
1590	→→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1591	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1478, 1590
1592	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-2
1593	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1591, 1592
1594	→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1589, 1593
1595	→→¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into pm2.18
1596	¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1594, 1595
1597	→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-1
1598	→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1596, 1597
1599	→→¬¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1600	→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1598, 1599
1601	→→¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑] into ax-3
1602	→¬¬↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1600, 1601
1603	↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 1596, 1602	dfbi1
1604	→¬→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓] into simplim
1605	→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens df-bi, 1604
1606	→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜓𝜑] into simplim
1607	→→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1608	→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓	Modus ponens 1606, 1607
1609	→→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜑𝜓→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2
1610	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜑𝜓	Modus ponens 1608, 1609
1611	→↔𝜑𝜓→𝜑𝜓	Modus ponens 1605, 1610	biimp
1612	→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into simprim
1613	→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into biimp
1614	→→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1615	→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑	Modus ponens 1612, 1614
1616	→→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
1617	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Modus ponens 1615, 1616
1618	→↔𝜑𝜓→𝜓𝜑	Modus ponens 1605, 1617	biimpr
1619	→→𝜓𝜑→→𝜑𝜓↔𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗𝜑] into impbi
1620	→→𝜑𝜓→→𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1
1621	→→→𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜓𝜑→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1622	→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓	Modus ponens 1620, 1621
1623	→→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜑→𝜑𝜓→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜑→𝜑𝜓] into ax-2
1624	→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓	Modus ponens 1622, 1623
1625	→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓	Modus ponens biimp, 1624
1626	→→→𝜓𝜑→→𝜑𝜓↔𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2
1627	→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑	Modus ponens 1619, 1626
1628	→→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑	Subs [𝜑↗→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1629	→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑	Modus ponens 1627, 1628
1630	→→↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜓𝜑→→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜑→𝜑𝜓, 𝜒↗→→𝜓𝜑↔𝜓𝜑] into ax-2
1631	→→↔𝜑𝜓→→𝜓𝜑→𝜑𝜓→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑	Modus ponens 1629, 1630
1632	→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑	Modus ponens 1625, 1631
1633	→→𝜓𝜑→𝜓𝜑	Subs [𝜑↗→𝜓𝜑] into id
1634	→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1635	→→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1
1636	→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Modus ponens 1634, 1635
1637	→→→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→↔𝜑𝜓→𝜓𝜑] into ax-2
1638	→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Modus ponens 1636, 1637
1639	→→↔𝜑𝜓→→𝜓𝜑↔𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜓𝜑] into ax-2
1640	→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1632, 1639
1641	→→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1
1642	→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1640, 1641
1643	→→→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→↔𝜑𝜓→𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2
1644	→→→𝜓𝜑→↔𝜑𝜓→𝜓𝜑→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1642, 1643
1645	→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1634, 1644
1646	→→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1647	→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1645, 1646
1648	→→↔𝜑𝜓→→𝜓𝜑→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2
1649	→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1647, 1648
1650	→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Modus ponens biimpr, 1649
1651	→↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓] into id
1652	→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1653	→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1654	→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓	Modus ponens 1652, 1653
1655	→→↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜓] into ax-2
1656	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓	Modus ponens 1654, 1655
1657	→→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2
1658	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1650, 1657
1659	→→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1660	→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1658, 1659
1661	→→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔𝜓𝜑] into ax-2
1662	→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1660, 1661
1663	→↔𝜑𝜓↔𝜓𝜑	Modus ponens 1651, 1658	bicom1
1664	→↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into bicom1
1665	→→↔𝜑𝜓↔𝜓𝜑→→↔𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into impbi
1666	→→↔𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑	Modus ponens bicom1, 1665
1667	↔↔𝜑𝜓↔𝜓𝜑	Modus ponens 1664, 1666	bicom
1668	→→𝜑𝜑→→𝜑𝜑↔𝜑𝜑	Subs [𝜓↗𝜑] into impbi
1669	→→𝜑𝜑↔𝜑𝜑	Modus ponens id, 1668
1670	↔𝜑𝜑	Modus ponens id, 1669	biid
1671	↔𝜓𝜓	Subs [𝜑↗𝜓] into biid
1672	→↔𝜓𝜓→𝜑↔𝜓𝜓	Subs [𝜑↗↔𝜓𝜓, 𝜓↗𝜑] into ax-1
1673	→𝜑↔𝜓𝜓	Modus ponens 1671, 1672	biidd
1674	→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
1675	→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗𝜑] into ax-1
1676	→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Modus ponens 1674, 1675
1677	→→𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜑→𝜓𝜑→𝜑→→𝜑𝜓→𝜓𝜑	Subs [𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2
1678	→→𝜑→𝜓𝜑→𝜑→→𝜑𝜓→𝜓𝜑	Modus ponens 1676, 1677
1679	→𝜑→→𝜑𝜓→𝜓𝜑	Modus ponens ax-1, 1678
1680	→→→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
1681	→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens impbi, 1680
1682	→→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
1683	→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens 1681, 1682
1684	→→𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜑𝜓↔𝜑𝜓	Subs [𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2
1685	→→𝜑→→𝜑𝜓→𝜓𝜑→𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens 1683, 1684
1686	→𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens 1679, 1685
1687	→→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1688	→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓	Modus ponens 533, 1687
1689	→→→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into ax-2
1690	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜑𝜓	Modus ponens 1688, 1689
1691	→→𝜑→→𝜑𝜓↔𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
1692	→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 1686, 1691
1693	→→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
1694	→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 1692, 1693
1695	→→→𝜑𝜓→→𝜑→𝜑𝜓→𝜑↔𝜑𝜓→→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
1696	→→→𝜑𝜓→𝜑→𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 1694, 1695
1697	→→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 533, 1696
1698	→→→𝜑𝜓→𝜑↔𝜑𝜓→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓] into ax-1
1699	→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 1697, 1698
1700	→→𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
1701	→→𝜓→𝜑𝜓→𝜓→𝜑↔𝜑𝜓	Modus ponens 1699, 1700
1702	→𝜓→𝜑↔𝜑𝜓	Modus ponens 208, 1701
1703	→→𝜑→𝜓𝜑→𝜑→𝜑→𝜓𝜑	Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗𝜑] into ax-1
1704	→𝜑→𝜑→𝜓𝜑	Modus ponens ax-1, 1703
1705	→→𝜑→𝜑→𝜓𝜑→→𝜑𝜑→𝜑→𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗→𝜓𝜑] into ax-2
1706	→→𝜑𝜑→𝜑→𝜓𝜑	Modus ponens 1704, 1705
1707	→→𝜓→𝜑↔𝜑𝜓→→𝜓𝜑→𝜓↔𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗↔𝜑𝜓] into ax-2
1708	→→𝜓𝜑→𝜓↔𝜑𝜓	Modus ponens 1702, 1707
1709	→→→𝜓𝜑→𝜓↔𝜑𝜓→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓	Subs [𝜑↗→→𝜓𝜑→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
1710	→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓	Modus ponens 1708, 1709
1711	→→𝜑→→𝜓𝜑→𝜓↔𝜑𝜓→→𝜑→𝜓𝜑→𝜑→𝜓↔𝜑𝜓	Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓↔𝜑𝜓] into ax-2
1712	→→𝜑→𝜓𝜑→𝜑→𝜓↔𝜑𝜓	Modus ponens 1710, 1711
1713	→𝜑→𝜓↔𝜑𝜓	Modus ponens ax-1, 1712	pm5.1im
1714	→→𝜓𝜓→→𝜑𝜑→𝜓𝜓	Subs [𝜑↗→𝜓𝜓, 𝜓↗→𝜑𝜑] into ax-1
1715	→→𝜑𝜑→𝜓𝜓	Modus ponens 10, 1714
1716	→→𝜑𝜑→→𝜓𝜓→𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜓𝜓] into ax-1
1717	→→𝜓𝜓→𝜑𝜑	Modus ponens id, 1716
1718	→→→𝜑𝜑→𝜓𝜓→→→𝜓𝜓→𝜑𝜑↔→𝜑𝜑→𝜓𝜓	Subs [𝜑↗→𝜑𝜑, 𝜓↗→𝜓𝜓] into impbi
1719	→→→𝜓𝜓→𝜑𝜑↔→𝜑𝜑→𝜓𝜓	Modus ponens 1715, 1718
1720	↔→𝜑𝜑→𝜓𝜓	Modus ponens 1717, 1719	monothetic
1721	→↔𝜓𝜒→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into biimp
1722	→→↔𝜓𝜒→𝜓𝜒→𝜑→↔𝜓𝜒→𝜓𝜒	Subs [𝜑↗→↔𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
1723	→𝜑→↔𝜓𝜒→𝜓𝜒	Modus ponens 1721, 1722
1724	→→𝜑→↔𝜓𝜒→𝜓𝜒→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜓↗↔𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
1725	→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 1723, 1724
1726	→→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1727	→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens ax-2, 1726
1728	→→→𝜑↔𝜓𝜒→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
1729	→→→𝜑↔𝜓𝜒→𝜑→𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 1727, 1728
1730	→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 1725, 1729
1731	→↔𝜓𝜒→𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜒] into biimpr
1732	→→↔𝜓𝜒→𝜒𝜓→𝜑→↔𝜓𝜒→𝜒𝜓	Subs [𝜑↗→↔𝜓𝜒→𝜒𝜓, 𝜓↗𝜑] into ax-1
1733	→𝜑→↔𝜓𝜒→𝜒𝜓	Modus ponens 1731, 1732
1734	→→𝜑→↔𝜓𝜒→𝜒𝜓→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓	Subs [𝜓↗↔𝜓𝜒, 𝜒↗→𝜒𝜓] into ax-2
1735	→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓	Modus ponens 1733, 1734
1736	→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓	Subs [𝜓↗𝜒, 𝜒↗𝜓] into ax-2
1737	→→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1738	→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓	Modus ponens 1736, 1737
1739	→→→𝜑↔𝜓𝜒→→𝜑→𝜒𝜓→→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑→𝜒𝜓, 𝜒↗→→𝜑𝜒→𝜑𝜓] into ax-2
1740	→→→𝜑↔𝜓𝜒→𝜑→𝜒𝜓→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓	Modus ponens 1738, 1739
1741	→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓	Modus ponens 1735, 1740
1742	→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into impbi
1743	→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜒→𝜑𝜓, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
1744	→→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1745	→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓	Modus ponens 1743, 1744
1746	→→→𝜑↔𝜓𝜒→→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓] into ax-2
1747	→→→𝜑↔𝜓𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓	Modus ponens 1745, 1746
1748	→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓	Modus ponens 1741, 1747
1749	→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2
1750	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1742, 1749
1751	→→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1752	→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1750, 1751
1753	→→→𝜑↔𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓, 𝜒↗→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1754	→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1752, 1753
1755	→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1748, 1754
1756	→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1757	→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
1758	→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 1756, 1757
1759	→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
1760	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 1758, 1759
1761	→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2
1762	→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1755, 1761
1763	→→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
1764	→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1762, 1763
1765	→→→→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1766	→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1764, 1765
1767	→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1756, 1766
1768	→→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1769	→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1767, 1768
1770	→→→𝜑↔𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1771	→→→𝜑↔𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1769, 1770
1772	→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1730, 1771
1773	→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒] into id
1774	→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1775	→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1776	→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 1774, 1775
1777	→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒] into ax-2
1778	→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 1776, 1777
1779	→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗↔→𝜑𝜓→𝜑𝜒] into ax-2
1780	→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1772, 1779
1781	→→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
1782	→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1780, 1781
1783	→→→𝜑↔𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒, 𝜒↗→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1784	→→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1782, 1783
1785	→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1773, 1780
1786	→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into biimp
1787	→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1788	→→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-1
1789	→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 1787, 1788
1790	→→𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2
1791	→→𝜓→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 1789, 1790
1792	→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 208, 1791
1793	→→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
1794	→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 1786, 1793
1795	→→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-1
1796	→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 1794, 1795
1797	→→𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2
1798	→→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 1796, 1797
1799	→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 1792, 1798
1800	→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒] into id
1801	→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1802	→→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1803	→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒	Modus ponens 1801, 1802
1804	→→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓↔→𝜑𝜓→𝜑𝜒] into ax-2
1805	→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒	Modus ponens 1803, 1804
1806	→→𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜒] into ax-2
1807	→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 1799, 1806
1808	→→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Subs [𝜑↗→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1809	→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 1807, 1808
1810	→→↔→𝜑𝜓→𝜑𝜒→→𝜓↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜓→𝜑𝜒] into ax-2
1811	→→↔→𝜑𝜓→𝜑𝜒→𝜓↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 1809, 1810
1812	→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒	Modus ponens 1801, 1811
1813	→→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒	Subs [𝜑↗→𝜑→→𝜑𝜒𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1814	→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒	Modus ponens 264, 1813
1815	→→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Subs [𝜑↗→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1816	→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Modus ponens 267, 1815
1817	→→↔→𝜑𝜓→𝜑𝜒→→𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓→𝜑𝜒] into ax-2
1818	→→↔→𝜑𝜓→𝜑𝜒→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Modus ponens 1816, 1817
1819	→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒	Modus ponens 1812, 1818
1820	→→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1821	→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 277, 1820
1822	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒] into ax-2
1823	→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜒𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 1821, 1822
1824	→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒	Modus ponens 1814, 1823
1825	→→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1826	→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 283, 1825
1827	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜓→𝜑𝜒→𝜓𝜒, 𝜒↗→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒] into ax-2
1828	→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜓→𝜑𝜒→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 1826, 1827
1829	→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 1824, 1828
1830	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓→𝜑𝜒→𝜑→𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓→𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
1831	→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 1829, 1830
1832	→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 1819, 1831
1833	→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into biimpr
1834	→𝜒→𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜑] into ax-1
1835	→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1836	→→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒, 𝜓↗𝜒] into ax-1
1837	→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 1835, 1836
1838	→→𝜒→→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒] into ax-2
1839	→→𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 1837, 1838
1840	→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒	Modus ponens 1834, 1839
1841	→→↔→𝜑𝜓→𝜑𝜒→→𝜑𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into ax-2
1842	→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 1833, 1841
1843	→→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓, 𝜓↗𝜒] into ax-1
1844	→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 1842, 1843
1845	→→𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒, 𝜒↗→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓] into ax-2
1846	→→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜒→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 1844, 1845
1847	→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓	Modus ponens 1840, 1846
1848	→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗𝜒] into ax-1
1849	→→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1850	→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1848, 1849
1851	→→↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜒↔→𝜑𝜓→𝜑𝜒] into ax-2
1852	→→↔→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1850, 1851
1853	→→𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑𝜓→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑𝜓] into ax-2
1854	→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓	Modus ponens 1847, 1853
1855	→→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓	Subs [𝜑↗→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1856	→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓	Modus ponens 1854, 1855
1857	→→↔→𝜑𝜓→𝜑𝜒→→𝜒↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜒↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜒→𝜑𝜓] into ax-2
1858	→→↔→𝜑𝜓→𝜑𝜒→𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓	Modus ponens 1856, 1857
1859	→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓	Modus ponens 1848, 1858
1860	→→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→𝜑→→𝜑𝜓𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1861	→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓	Modus ponens pm2.27, 1860
1862	→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓	Subs [𝜑↗→𝜒→𝜑𝜓, 𝜓↗𝜑] into ax-1
1863	→→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓	Subs [𝜑↗→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1864	→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓	Modus ponens 1862, 1863
1865	→→↔→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜓→𝜑→𝜒→𝜑𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜑→𝜒→𝜑𝜓] into ax-2
1866	→→↔→𝜑𝜓→𝜑𝜒→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓	Modus ponens 1864, 1865
1867	→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓	Modus ponens 1859, 1866
1868	→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓	Subs [𝜑↗→𝜑𝜓] into imim2
1869	→→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓	Subs [𝜑↗→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓, 𝜓↗𝜑] into ax-1
1870	→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓	Modus ponens 1868, 1869
1871	→→𝜑→→→𝜑𝜓𝜓→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓	Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗→→𝜒→𝜑𝜓→𝜒𝜓] into ax-2
1872	→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓	Modus ponens 1870, 1871
1873	→→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓	Subs [𝜑↗→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1874	→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓	Modus ponens 1872, 1873
1875	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜑𝜓𝜓→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜑𝜓𝜓, 𝜒↗→𝜑→→𝜒→𝜑𝜓→𝜒𝜓] into ax-2
1876	→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜑𝜓𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓	Modus ponens 1874, 1875
1877	→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓	Modus ponens 1861, 1876
1878	→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓	Subs [𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2
1879	→→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓	Subs [𝜑↗→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1880	→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓	Modus ponens 1878, 1879
1881	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜒→𝜑𝜓→𝜒𝜓, 𝜒↗→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓] into ax-2
1882	→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒→𝜑𝜓→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓	Modus ponens 1880, 1881
1883	→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓	Modus ponens 1877, 1882
1884	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒→𝜑𝜓→𝜑→𝜒𝜓→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜒→𝜑𝜓, 𝜒↗→𝜑→𝜒𝜓] into ax-2
1885	→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒→𝜑𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓	Modus ponens 1883, 1884
1886	→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓	Modus ponens 1867, 1885
1887	→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into impbi
1888	→→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒, 𝜓↗𝜑] into ax-1
1889	→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒	Modus ponens 1887, 1888
1890	→→𝜑→→𝜓𝜒→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒	Subs [𝜓↗→𝜓𝜒, 𝜒↗→→𝜒𝜓↔𝜓𝜒] into ax-2
1891	→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒	Modus ponens 1889, 1890
1892	→→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1893	→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒	Modus ponens 1891, 1892
1894	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜓𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→𝜑→→𝜒𝜓↔𝜓𝜒] into ax-2
1895	→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒	Modus ponens 1893, 1894
1896	→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒	Modus ponens 1832, 1895
1897	→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒	Subs [𝜓↗→𝜒𝜓, 𝜒↗↔𝜓𝜒] into ax-2
1898	→→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into ax-1
1899	→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒	Modus ponens 1897, 1898
1900	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→→𝜒𝜓↔𝜓𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→→𝜒𝜓↔𝜓𝜒, 𝜒↗→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒] into ax-2
1901	→→↔→𝜑𝜓→𝜑𝜒→𝜑→→𝜒𝜓↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒	Modus ponens 1899, 1900
1902	→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒	Modus ponens 1896, 1901
1903	→→↔→𝜑𝜓→𝜑𝜒→→𝜑→𝜒𝜓→𝜑↔𝜓𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑→𝜒𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
1904	→→↔→𝜑𝜓→𝜑𝜒→𝜑→𝜒𝜓→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 1902, 1903
1905	→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 1886, 1904
1906	→→→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into impbi
1907	→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1785, 1906
1908	↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 1905, 1907	pm5.74
1909	→→𝜑¬¬𝜑→→¬¬𝜑𝜑↔𝜑¬¬𝜑	Subs [𝜓↗¬¬𝜑] into impbi
1910	→→¬¬𝜑𝜑↔𝜑¬¬𝜑	Modus ponens notnot, 1909
1911	↔𝜑¬¬𝜑	Modus ponens notnotr, 1910	notnotb
1912	→→→𝜑𝜓→¬𝜓¬𝜑→→→¬𝜓¬𝜑→𝜑𝜓↔→𝜑𝜓→¬𝜓¬𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬𝜓¬𝜑] into impbi
1913	→→→¬𝜓¬𝜑→𝜑𝜓↔→𝜑𝜓→¬𝜓¬𝜑	Modus ponens con3, 1912
1914	↔→𝜑𝜓→¬𝜓¬𝜑	Modus ponens 316, 1913	con34b
1915	↔𝜓¬¬𝜓	Subs [𝜑↗𝜓] into notnotb
1916	→↔𝜑¬¬𝜑↔¬¬𝜑𝜑	Subs [𝜓↗¬¬𝜑] into bicom1
1917	↔¬¬𝜑𝜑	Modus ponens notnotb, 1916
1918	→↔¬¬𝜑𝜑→↔𝜑𝜓↔¬¬𝜑𝜑	Subs [𝜑↗↔¬¬𝜑𝜑, 𝜓↗↔𝜑𝜓] into ax-1
1919	→↔𝜑𝜓↔¬¬𝜑𝜑	Modus ponens 1917, 1918
1920	↔→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗𝜑] into pm5.74
1921	→↔→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜑, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑] into biimp
1922	→→↔𝜑𝜓↔¬¬𝜑𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑	Modus ponens 1920, 1921
1923	↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑	Modus ponens 1919, 1922
1924	↔→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74
1925	→↔→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp
1926	→→↔𝜑𝜓↔𝜑𝜓↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 1924, 1925
1927	↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 1651, 1926
1928	→↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜓] into biimp
1929	→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 1927, 1928
1930	→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑] into biimp
1931	→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑	Modus ponens 1923, 1930
1932	→→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into ax-1
1933	→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 1929, 1932
1934	→→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into ax-2
1935	→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Modus ponens 1933, 1934
1936	→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Modus ponens 1931, 1935
1937	→↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜓] into bicom1
1938	↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 1927, 1937
1939	→↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜑] into biimp
1940	→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 1938, 1939
1941	→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜑] into bicom1
1942	↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑	Modus ponens 1923, 1941
1943	→↔→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜑] into biimp
1944	→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑	Modus ponens 1942, 1943
1945	→→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into ax-1
1946	→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑	Modus ponens 1944, 1945
1947	→→→↔𝜑𝜓𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓¬¬𝜑→→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2
1948	→→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 1946, 1947
1949	→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 1940, 1948
1950	→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into impbi
1951	→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Modus ponens 1936, 1950
1952	↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Modus ponens 1949, 1951
1953	↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗𝜓] into pm5.74
1954	→↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓] into bicom1
1955	↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓	Modus ponens 1953, 1954
1956	→↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓	Subs [𝜑↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔¬¬𝜑𝜓] into biimp
1957	→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→↔𝜑𝜓↔¬¬𝜑𝜓	Modus ponens 1955, 1956
1958	→↔𝜑𝜓↔¬¬𝜑𝜓	Modus ponens 1952, 1957
1959	→↔𝜓¬¬𝜓→↔𝜑𝜓↔𝜓¬¬𝜓	Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
1960	→↔𝜑𝜓↔𝜓¬¬𝜓	Modus ponens 1915, 1959
1961	→↔→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓] into biimp
1962	→→↔𝜑𝜓↔¬¬𝜑𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Modus ponens 1953, 1961
1963	↔→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74
1964	→↔→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜓¬¬𝜓, 𝜓↗↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓] into biimp
1965	→→↔𝜑𝜓↔𝜓¬¬𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Modus ponens 1963, 1964
1966	↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Modus ponens 1960, 1965
1967	→↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓] into biimp
1968	→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Modus ponens 1966, 1967
1969	→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into biimp
1970	→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into ax-1
1971	→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓	Modus ponens 1968, 1970
1972	→→→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜓] into ax-2
1973	→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓	Modus ponens 1971, 1972
1974	→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓	Modus ponens 1936, 1973
1975	→↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜓↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓] into bicom1
1976	↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓	Modus ponens 1966, 1975
1977	→↔→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓𝜓] into biimp
1978	→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓	Modus ponens 1976, 1977
1979	→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓𝜓] into bicom1
1980	↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 1952, 1979
1981	→↔→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜑] into biimp
1982	→→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜓] into ax-1
1983	→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 1949, 1982
1984	→→→↔𝜑𝜓¬¬𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓¬¬𝜑→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2
1985	→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 1983, 1984
1986	→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 1978, 1985
1987	→→→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬𝜑, 𝜓↗→↔𝜑𝜓¬¬𝜓] into impbi
1988	→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓	Modus ponens 1974, 1987
1989	↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓	Modus ponens 1986, 1988
1990	↔→↔𝜑𝜓↔¬¬𝜑¬¬𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜑, 𝜒↗¬¬𝜓] into pm5.74
1991	→↔→↔𝜑𝜓↔¬¬𝜑¬¬𝜓↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓	Subs [𝜑↗→↔𝜑𝜓↔¬¬𝜑¬¬𝜓, 𝜓↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓] into bicom1
1992	↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓	Modus ponens 1990, 1991
1993	→↔↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓	Subs [𝜑↗↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓, 𝜓↗→↔𝜑𝜓↔¬¬𝜑¬¬𝜓] into biimp
1994	→↔→↔𝜑𝜓¬¬𝜑→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓↔¬¬𝜑¬¬𝜓	Modus ponens 1992, 1993
1995	→↔𝜑𝜓↔¬¬𝜑¬¬𝜓	Modus ponens 1989, 1994
1996	→¬¬𝜓¬¬𝜓	Subs [𝜑↗¬¬𝜓] into id
1997	↔↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗¬¬𝜓] into bicom
1998	→↔↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑	Subs [𝜑↗↔¬¬𝜑¬¬𝜓, 𝜓↗↔¬¬𝜓¬¬𝜑] into biimp
1999	→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑	Modus ponens 1997, 1998
2000	→→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑	Subs [𝜑↗→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2001	→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑	Modus ponens 1999, 2000
2002	→→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓↔¬¬𝜓¬¬𝜑→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓↔¬¬𝜓¬¬𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜑¬¬𝜓, 𝜒↗↔¬¬𝜓¬¬𝜑] into ax-2
2003	→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓↔¬¬𝜓¬¬𝜑	Modus ponens 2001, 2002
2004	→↔𝜑𝜓↔¬¬𝜓¬¬𝜑	Modus ponens 1995, 2003
2005	→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜑] into biimp
2006	→→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑	Subs [𝜑↗→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2007	→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑	Modus ponens 2005, 2006
2008	→→↔𝜑𝜓→↔¬¬𝜓¬¬𝜑→¬¬𝜓¬¬𝜑→→↔𝜑𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬¬𝜓¬¬𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜓¬¬𝜑, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2
2009	→→↔𝜑𝜓↔¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬¬𝜓¬¬𝜑	Modus ponens 2007, 2008
2010	→↔𝜑𝜓→¬¬𝜓¬¬𝜑	Modus ponens 2004, 2009
2011	→¬¬𝜓→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2012	→→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗→¬¬𝜓→↔𝜑𝜓¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1
2013	→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓	Modus ponens 2011, 2012
2014	→→¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓→→¬¬𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜓] into ax-2
2015	→→¬¬𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜓	Modus ponens 2013, 2014
2016	→→↔𝜑𝜓→¬¬𝜓¬¬𝜑→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜓, 𝜒↗¬¬𝜑] into ax-2
2017	→→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑, 𝜓↗¬¬𝜓] into ax-1
2018	→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 1986, 2017
2019	→→¬¬𝜓→→↔𝜑𝜓¬¬𝜓→↔𝜑𝜓¬¬𝜑→→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗→↔𝜑𝜓¬¬𝜓, 𝜒↗→↔𝜑𝜓¬¬𝜑] into ax-2
2020	→→¬¬𝜓→↔𝜑𝜓¬¬𝜓→¬¬𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 2018, 2019
2021	→¬¬𝜓→↔𝜑𝜓¬¬𝜑	Modus ponens 2011, 2020
2022	→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
2023	→→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2024	→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓	Modus ponens 2022, 2023
2025	→→↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬𝜓↔𝜑𝜓] into ax-2
2026	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓	Modus ponens 2024, 2025
2027	→→¬¬𝜓→↔𝜑𝜓¬¬𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬𝜑] into ax-2
2028	→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑	Modus ponens 2021, 2027
2029	→→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑	Subs [𝜑↗→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2030	→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑	Modus ponens 2028, 2029
2031	→→↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬𝜑→→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓¬¬𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2
2032	→→↔𝜑𝜓→¬¬𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬𝜓¬¬𝜑	Modus ponens 2030, 2031
2033	→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into ax-3
2034	→→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2035	→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓	Modus ponens 2033, 2034
2036	→→↔𝜑𝜓→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→→↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜓¬¬𝜑, 𝜒↗→¬𝜑¬𝜓] into ax-2
2037	→→↔𝜑𝜓→¬¬𝜓¬¬𝜑→↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 2035, 2036
2038	→↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 2010, 2037
2039	→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗¬¬𝜓] into biimp
2040	→→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2041	→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓	Modus ponens 2039, 2040
2042	→→↔𝜑𝜓→↔¬¬𝜑¬¬𝜓→¬¬𝜑¬¬𝜓→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬¬𝜑¬¬𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
2043	→→↔𝜑𝜓↔¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 2041, 2042
2044	→↔𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 1995, 2043
2045	→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2046	→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Modus ponens 494, 2045
2047	→→↔𝜑𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→↔𝜑𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬𝜓¬𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
2048	→→↔𝜑𝜓→¬¬𝜑¬¬𝜓→↔𝜑𝜓→¬𝜓¬𝜑	Modus ponens 2046, 2047
2049	→↔𝜑𝜓→¬𝜓¬𝜑	Modus ponens 2044, 2048
2050	→→¬𝜑¬𝜓→→¬𝜓¬𝜑↔¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into impbi
2051	→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜑¬𝜓] into ax-1
2052	→→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2053	→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2051, 2052
2054	→→↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜑¬𝜓→¬𝜓¬𝜑→→↔𝜑𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→→¬𝜑¬𝜓→¬𝜓¬𝜑] into ax-2
2055	→→↔𝜑𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2053, 2054
2056	→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2049, 2055
2057	→→→¬𝜑¬𝜓→→¬𝜓¬𝜑↔¬𝜑¬𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗↔¬𝜑¬𝜓] into ax-2
2058	→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓	Modus ponens 2050, 2057
2059	→→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2060	→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓	Modus ponens 2058, 2059
2061	→→↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜓¬𝜑→→¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜒↗→→¬𝜑¬𝜓↔¬𝜑¬𝜓] into ax-2
2062	→→↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜓¬𝜑→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓	Modus ponens 2060, 2061
2063	→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓	Modus ponens 2056, 2062
2064	→→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓] into id
2065	→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2066	→→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1
2067	→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 2065, 2066
2068	→→→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓→¬𝜑¬𝜓] into ax-2
2069	→→→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 2067, 2068
2070	→→↔𝜑𝜓→→¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗↔¬𝜑¬𝜓] into ax-2
2071	→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2063, 2070
2072	→→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1
2073	→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2071, 2072
2074	→→→¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→↔𝜑𝜓→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2
2075	→→→¬𝜑¬𝜓→↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2073, 2074
2076	→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2065, 2075
2077	→→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2078	→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2076, 2077
2079	→→↔𝜑𝜓→→¬𝜑¬𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2
2080	→→↔𝜑𝜓→¬𝜑¬𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2078, 2079
2081	→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2038, 2080
2082	→→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔¬𝜑¬𝜓] into ax-2
2083	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2081, 2082
2084	→→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2085	→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2083, 2084
2086	→→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔¬𝜑¬𝜓] into ax-2
2087	→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2085, 2086
2088	→↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 1651, 2083
2089	→↔¬𝜑¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔¬𝜑¬𝜓] into id
2090	↔↔¬𝜑¬𝜓↔¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into bicom
2091	→↔↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓↔¬𝜓¬𝜑	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜓¬𝜑] into biimp
2092	→↔¬𝜑¬𝜓↔¬𝜓¬𝜑	Modus ponens 2090, 2091
2093	→→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑¬𝜓↔¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2094	→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑	Modus ponens 2092, 2093
2095	→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔¬𝜓¬𝜑] into ax-2
2096	→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜓¬𝜑	Modus ponens 2094, 2095
2097	→↔¬𝜓¬𝜑→¬𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into biimp
2098	→→↔¬𝜓¬𝜑→¬𝜓¬𝜑→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑	Subs [𝜑↗→↔¬𝜓¬𝜑→¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2099	→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑	Modus ponens 2097, 2098
2100	→→↔¬𝜑¬𝜓→↔¬𝜓¬𝜑→¬𝜓¬𝜑→→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜓¬𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2
2101	→→↔¬𝜑¬𝜓↔¬𝜓¬𝜑→↔¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2099, 2100
2102	→↔¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2092, 2101
2103	→¬𝜓→↔¬𝜑¬𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2104	→→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓	Subs [𝜑↗→¬𝜓→↔¬𝜑¬𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
2105	→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓	Modus ponens 2103, 2104
2106	→→¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→↔¬𝜑¬𝜓¬𝜓] into ax-2
2107	→→¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜓	Modus ponens 2105, 2106
2108	→→↔¬𝜑¬𝜓→¬𝜓¬𝜑→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
2109	→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑	Modus ponens 2102, 2108
2110	→→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑	Subs [𝜑↗→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
2111	→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑	Modus ponens 2109, 2110
2112	→→¬𝜓→→↔¬𝜑¬𝜓¬𝜓→↔¬𝜑¬𝜓¬𝜑→→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→↔¬𝜑¬𝜓¬𝜓, 𝜒↗→↔¬𝜑¬𝜓¬𝜑] into ax-2
2113	→→¬𝜓→↔¬𝜑¬𝜓¬𝜓→¬𝜓→↔¬𝜑¬𝜓¬𝜑	Modus ponens 2111, 2112
2114	→¬𝜓→↔¬𝜑¬𝜓¬𝜑	Modus ponens 2103, 2113
2115	→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
2116	→→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2117	→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓	Modus ponens 2115, 2116
2118	→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→¬𝜓↔¬𝜑¬𝜓] into ax-2
2119	→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓	Modus ponens 2117, 2118
2120	→→¬𝜓→↔¬𝜑¬𝜓¬𝜑→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗¬𝜑] into ax-2
2121	→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2114, 2120
2122	→→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2123	→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2121, 2122
2124	→→↔¬𝜑¬𝜓→→¬𝜓↔¬𝜑¬𝜓→¬𝜓¬𝜑→→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜓↔¬𝜑¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
2125	→→↔¬𝜑¬𝜓→¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜓¬𝜑	Modus ponens 2123, 2124
2126	→→→¬𝜓¬𝜑→𝜑𝜓→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓	Subs [𝜑↗→→¬𝜓¬𝜑→𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2127	→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓	Modus ponens 316, 2126
2128	→→↔¬𝜑¬𝜓→→¬𝜓¬𝜑→𝜑𝜓→→↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
2129	→→↔¬𝜑¬𝜓→¬𝜓¬𝜑→↔¬𝜑¬𝜓→𝜑𝜓	Modus ponens 2127, 2128
2130	→↔¬𝜑¬𝜓→𝜑𝜓	Modus ponens 2102, 2129
2131	→↔¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into biimp
2132	→→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2133	→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 2131, 2132
2134	→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
2135	→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 2133, 2134
2136	→→→¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑	Subs [𝜑↗→→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2137	→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑	Modus ponens ax-3, 2136
2138	→→↔¬𝜑¬𝜓→→¬𝜑¬𝜓→𝜓𝜑→→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→𝜓𝜑	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→𝜓𝜑] into ax-2
2139	→→↔¬𝜑¬𝜓→¬𝜑¬𝜓→↔¬𝜑¬𝜓→𝜓𝜑	Modus ponens 2137, 2138
2140	→↔¬𝜑¬𝜓→𝜓𝜑	Modus ponens 2131, 2139
2141	→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2142	→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Modus ponens 1674, 2141
2143	→→↔¬𝜑¬𝜓→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→↔¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2
2144	→→↔¬𝜑¬𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑	Modus ponens 2142, 2143
2145	→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑	Modus ponens 2140, 2144
2146	→→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2147	→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens 1681, 2146
2148	→→↔¬𝜑¬𝜓→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2
2149	→→↔¬𝜑¬𝜓→→𝜑𝜓→𝜓𝜑→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓	Modus ponens 2147, 2148
2150	→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓	Modus ponens 2145, 2149
2151	→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2152	→→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
2153	→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓	Modus ponens 2151, 2152
2154	→→→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓→𝜑𝜓] into ax-2
2155	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓	Modus ponens 2153, 2154
2156	→→↔¬𝜑¬𝜓→→𝜑𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
2157	→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2150, 2156
2158	→→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
2159	→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2157, 2158
2160	→→→𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→↔¬𝜑¬𝜓→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2
2161	→→→𝜑𝜓→↔¬𝜑¬𝜓→𝜑𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2159, 2160
2162	→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2151, 2161
2163	→→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2164	→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2162, 2163
2165	→→↔¬𝜑¬𝜓→→𝜑𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2
2166	→→↔¬𝜑¬𝜓→𝜑𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2164, 2165
2167	→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2130, 2166
2168	→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2169	→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2170	→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓	Modus ponens 2168, 2169
2171	→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗→↔¬𝜑¬𝜓↔¬𝜑¬𝜓] into ax-2
2172	→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓	Modus ponens 2170, 2171
2173	→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
2174	→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2167, 2173
2175	→→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into ax-1
2176	→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2174, 2175
2177	→→↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔¬𝜑¬𝜓, 𝜓↗→↔¬𝜑¬𝜓↔¬𝜑¬𝜓, 𝜒↗→↔¬𝜑¬𝜓↔𝜑𝜓] into ax-2
2178	→→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔¬𝜑¬𝜓→↔¬𝜑¬𝜓→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2176, 2177
2179	→↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 2089, 2174
2180	→→↔𝜑𝜓↔¬𝜑¬𝜓→→↔¬𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓↔¬𝜑¬𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into impbi
2181	→→↔¬𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2088, 2180
2182	↔↔𝜑𝜓↔¬𝜑¬𝜓	Modus ponens 2179, 2181	notbi
2183	→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜒𝜃] into simplim
2184	→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜃] into simprim
2185	→↔↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into biimp
2186	→→↔𝜑𝜓↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2187	→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑	Modus ponens bicom1, 2186
2188	→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓↔𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into ax-2
2189	→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑	Modus ponens 2187, 2188
2190	→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑	Modus ponens 2183, 2189
2191	→↔𝜓𝜑→𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗𝜑] into biimp
2192	→→↔𝜓𝜑→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑	Subs [𝜑↗→↔𝜓𝜑→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2193	→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑	Modus ponens 2191, 2192
2194	→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜓𝜑→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
2195	→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Modus ponens 2193, 2194
2196	→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Modus ponens 2190, 2195
2197	→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2198	→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓	Subs [𝜑↗→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓] into ax-1
2199	→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓	Modus ponens 2197, 2198
2200	→→𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→→𝜓𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓	Subs [𝜑↗𝜓, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓] into ax-2
2201	→→𝜓𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓	Modus ponens 2199, 2200
2202	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗𝜑] into ax-2
2203	→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑	Modus ponens 2196, 2202
2204	→→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑	Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑] into ax-1
2205	→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑	Modus ponens 2203, 2204
2206	→→𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑	Subs [𝜑↗𝜓, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑] into ax-2
2207	→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜓→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑	Modus ponens 2205, 2206
2208	→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑	Modus ponens 2197, 2207
2209	→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃] into id
2210	→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2211	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2212	→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃	Modus ponens 2210, 2211
2213	→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-2
2214	→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃	Modus ponens 2212, 2213
2215	→→𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃𝜑→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗𝜑] into ax-2
2216	→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Modus ponens 2208, 2215
2217	→→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Subs [𝜑↗→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2218	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Modus ponens 2216, 2217
2219	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→𝜓𝜑] into ax-2
2220	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑	Modus ponens 2218, 2219
2221	→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗𝜒] into idd
2222	→→𝜒𝜒→𝜑→𝜒𝜒	Subs [𝜑↗→𝜒𝜒, 𝜓↗𝜑] into ax-1
2223	→→→𝜒𝜒→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→𝜑→𝜒𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2224	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒	Modus ponens 2222, 2223
2225	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜑→𝜒𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜒𝜒, 𝜒↗→𝜑→𝜒𝜒] into ax-2
2226	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒	Modus ponens 2224, 2225
2227	→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒	Modus ponens 2221, 2226
2228	→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒	Subs [𝜓↗𝜒] into ax-2
2229	→→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2230	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒	Modus ponens 2228, 2229
2231	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑→𝜒𝜒, 𝜒↗→→𝜑𝜒→𝜑𝜒] into ax-2
2232	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒	Modus ponens 2230, 2231
2233	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒	Modus ponens 2227, 2232
2234	→→𝜓𝜑→→𝜑𝜒→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜒] into ax-1
2235	→→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜑, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2236	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑	Modus ponens 2234, 2235
2237	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜑] into ax-2
2238	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑	Modus ponens 2236, 2237
2239	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑	Modus ponens 2196, 2238
2240	→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜓↗𝜒, 𝜒↗𝜓] into imim2
2241	→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗→𝜑𝜒] into ax-1
2242	→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2240, 2241
2243	→→→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜓𝜑→𝜓𝜒] into ax-2
2244	→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2242, 2243
2245	→→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2246	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2244, 2245
2247	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜑𝜒, 𝜒↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒] into ax-2
2248	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2246, 2247
2249	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2233, 2248
2250	→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜒] into ax-2
2251	→→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2252	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Modus ponens 2250, 2251
2253	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒] into ax-2
2254	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Modus ponens 2252, 2253
2255	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Modus ponens 2249, 2254
2256	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜒] into ax-2
2257	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜑→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Modus ponens 2255, 2256
2258	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Modus ponens 2239, 2257
2259	→→↔𝜑𝜓→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→𝜑𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2260	→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓	Modus ponens biimp, 2259
2261	→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→𝜑𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
2262	→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓	Modus ponens 2260, 2261
2263	→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓	Modus ponens 2183, 2262
2264	→→→𝜒𝜒→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2265	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒	Modus ponens 51, 2264
2266	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜒𝜒→𝜓→𝜒𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
2267	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒	Modus ponens 2265, 2266
2268	→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒	Modus ponens 2221, 2267
2269	→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2270	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Modus ponens 57, 2269
2271	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
2272	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓→𝜒𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒	Modus ponens 2270, 2271
2273	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒	Modus ponens 2268, 2272
2274	→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2275	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 63, 2274
2276	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
2277	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓	Modus ponens 2275, 2276
2278	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓	Modus ponens 2263, 2277
2279	→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2280	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 72, 2279
2281	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
2282	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 2280, 2281
2283	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 2273, 2282
2284	→→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2285	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 78, 2284
2286	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2
2287	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 2285, 2286
2288	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 2283, 2287
2289	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
2290	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜓→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒	Modus ponens 2288, 2289
2291	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒	Modus ponens 2278, 2290
2292	→→→𝜑𝜒→𝜓𝜒→→→𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜓𝜒] into impbi
2293	→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→𝜓𝜒→𝜑𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2294	→→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2295	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Modus ponens 2293, 2294
2296	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒] into ax-2
2297	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Modus ponens 2295, 2296
2298	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Modus ponens 2291, 2297
2299	→→→→𝜑𝜒→𝜓𝜒→→→𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2300	→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Modus ponens 2292, 2299
2301	→→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2302	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Modus ponens 2300, 2301
2303	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒] into ax-2
2304	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Modus ponens 2302, 2303
2305	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Modus ponens 2298, 2304
2306	→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒] into id
2307	→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2308	→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2309	→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Modus ponens 2307, 2308
2310	→→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒] into ax-2
2311	→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒	Modus ponens 2309, 2310
2312	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2313	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2305, 2312
2314	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2315	→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2313, 2314
2316	→→→→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2
2317	→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2315, 2316
2318	→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2307, 2317
2319	→→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2320	→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2318, 2319
2321	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2
2322	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2320, 2321
2323	→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2258, 2322
2324	→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2325	→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2326	→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃	Modus ponens 2324, 2325
2327	→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-2
2328	→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃	Modus ponens 2326, 2327
2329	→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2330	→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2323, 2329
2331	→→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2332	→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2330, 2331
2333	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒] into ax-2
2334	→→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2332, 2333
2335	→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒	Modus ponens 2209, 2330
2336	→↔𝜒𝜃→𝜓↔𝜒𝜃	Subs [𝜑↗↔𝜒𝜃] into ax-1
2337	→→↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃	Subs [𝜑↗→↔𝜒𝜃→𝜓↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2338	→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃	Modus ponens 2336, 2337
2339	→→¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃→𝜓↔𝜒𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗↔𝜒𝜃, 𝜒↗→𝜓↔𝜒𝜃] into ax-2
2340	→→¬→↔𝜑𝜓¬↔𝜒𝜃↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃	Modus ponens 2338, 2339
2341	→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃	Modus ponens 2184, 2340
2342	↔→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into pm5.74
2343	→↔→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Subs [𝜑↗→𝜓↔𝜒𝜃, 𝜓↗↔→𝜓𝜒→𝜓𝜃] into biimp
2344	→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Modus ponens 2342, 2343
2345	→→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Subs [𝜑↗→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃] into ax-1
2346	→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Modus ponens 2344, 2345
2347	→→¬→↔𝜑𝜓¬↔𝜒𝜃→→𝜓↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓↔𝜒𝜃, 𝜒↗↔→𝜓𝜒→𝜓𝜃] into ax-2
2348	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Modus ponens 2346, 2347
2349	→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃	Modus ponens 2341, 2348
2350	↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜒, 𝜒↗→𝜓𝜒] into pm5.74
2351	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp
2352	→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Modus ponens 2350, 2351
2353	↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Modus ponens 2335, 2352
2354	↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜃] into pm5.74
2355	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into biimp
2356	→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜓𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2354, 2355
2357	↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2349, 2356
2358	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into biimp
2359	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2357, 2358
2360	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp
2361	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Modus ponens 2353, 2360
2362	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into ax-1
2363	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2359, 2362
2364	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into ax-2
2365	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2363, 2364
2366	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2361, 2365
2367	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into bicom1
2368	↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Modus ponens 2357, 2367
2369	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into biimp
2370	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒	Modus ponens 2368, 2369
2371	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒] into bicom1
2372	↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Modus ponens 2353, 2371
2373	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into biimp
2374	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Modus ponens 2372, 2373
2375	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Subs [𝜑↗→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into ax-1
2376	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Modus ponens 2374, 2375
2377	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒, 𝜒↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒] into ax-2
2378	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜒→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Modus ponens 2376, 2377
2379	→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒	Modus ponens 2370, 2378
2380	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into impbi
2381	→→→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2366, 2380
2382	↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Modus ponens 2379, 2381
2383	↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜓↗→𝜑𝜒, 𝜒↗→𝜓𝜃] into pm5.74
2384	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃] into bicom1
2385	↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2383, 2384
2386	→↔↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Subs [𝜑↗↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃, 𝜓↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃] into biimp
2387	→↔→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜃→𝜓𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2385, 2386
2388	→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2382, 2387
2389	→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜃] into pm3.2im
2390	→→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔𝜒𝜃] into ax-1
2391	→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2388, 2390
2392	→→↔𝜒𝜃→¬→↔𝜑𝜓¬↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Subs [𝜑↗↔𝜒𝜃, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗↔→𝜑𝜒→𝜓𝜃] into ax-2
2393	→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2391, 2392
2394	→→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Subs [𝜑↗→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃, 𝜓↗↔𝜑𝜓] into ax-1
2395	→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2393, 2394
2396	→→↔𝜑𝜓→→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃→→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃, 𝜒↗→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃] into ax-2
2397	→→↔𝜑𝜓→↔𝜒𝜃¬→↔𝜑𝜓¬↔𝜒𝜃→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2395, 2396
2398	→↔𝜑𝜓→↔𝜒𝜃↔→𝜑𝜒→𝜓𝜃	Modus ponens 2389, 2397	imbi12
2399	→→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2400	→→↔𝜓𝜑→𝜓𝜑→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑	Subs [𝜑↗→↔𝜓𝜑→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2401	→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑	Modus ponens 2191, 2400
2402	→→↔𝜑𝜓→↔𝜓𝜑→𝜓𝜑→→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
2403	→→↔𝜑𝜓↔𝜓𝜑→↔𝜑𝜓→𝜓𝜑	Modus ponens 2401, 2402
2404	→𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2405	→→𝜓→↔𝜑𝜓𝜓→𝜓→𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→𝜓→↔𝜑𝜓𝜓] into ax-1
2406	→𝜓→𝜓→↔𝜑𝜓𝜓	Modus ponens 2404, 2405
2407	→→𝜓→𝜓→↔𝜑𝜓𝜓→→𝜓𝜓→𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜒↗→↔𝜑𝜓𝜓] into ax-2
2408	→→𝜓𝜓→𝜓→↔𝜑𝜓𝜓	Modus ponens 2406, 2407
2409	→→↔𝜑𝜓→𝜓𝜑→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜒↗𝜑] into ax-2
2410	→→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-1
2411	→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 1940, 2410
2412	→→𝜓→→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→𝜓→↔𝜑𝜓𝜓→𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓𝜑] into ax-2
2413	→→𝜓→↔𝜑𝜓𝜓→𝜓→↔𝜑𝜓𝜑	Modus ponens 2411, 2412
2414	→𝜓→↔𝜑𝜓𝜑	Modus ponens 2404, 2413
2415	→↔𝜑𝜓→𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓] into ax-1
2416	→→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2417	→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓	Modus ponens 2415, 2416
2418	→→↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜓↔𝜑𝜓] into ax-2
2419	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓↔𝜑𝜓	Modus ponens 2417, 2418
2420	→→𝜓→↔𝜑𝜓𝜑→→𝜓↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗𝜑] into ax-2
2421	→→𝜓↔𝜑𝜓→𝜓𝜑	Modus ponens 2414, 2420
2422	→→→𝜓↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2423	→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑	Modus ponens 2421, 2422
2424	→→↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜓𝜑→→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜓𝜑] into ax-2
2425	→→↔𝜑𝜓→𝜓↔𝜑𝜓→↔𝜑𝜓→𝜓𝜑	Modus ponens 2423, 2424
2426	→↔𝜑𝜓→𝜒𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into idd
2427	→→→𝜒𝜒→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→𝜑→𝜒𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2428	→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒	Modus ponens 2222, 2427
2429	→→↔𝜑𝜓→→𝜒𝜒→𝜑→𝜒𝜒→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜑→𝜒𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜑→𝜒𝜒] into ax-2
2430	→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜑→𝜒𝜒	Modus ponens 2428, 2429
2431	→↔𝜑𝜓→𝜑→𝜒𝜒	Modus ponens 2426, 2430
2432	→→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2433	→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒	Modus ponens 2228, 2432
2434	→→↔𝜑𝜓→→𝜑→𝜒𝜒→→𝜑𝜒→𝜑𝜒→→↔𝜑𝜓→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑→𝜒𝜒, 𝜒↗→→𝜑𝜒→𝜑𝜒] into ax-2
2435	→→↔𝜑𝜓→𝜑→𝜒𝜒→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒	Modus ponens 2433, 2434
2436	→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒	Modus ponens 2431, 2435
2437	→→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2438	→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑	Modus ponens 2234, 2437
2439	→→↔𝜑𝜓→→𝜓𝜑→→𝜑𝜒→𝜓𝜑→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜑] into ax-2
2440	→→↔𝜑𝜓→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑	Modus ponens 2438, 2439
2441	→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑	Modus ponens biimpr, 2440
2442	→→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2443	→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2244, 2442
2444	→→↔𝜑𝜓→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜑𝜒, 𝜒↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒] into ax-2
2445	→→↔𝜑𝜓→→𝜑𝜒→𝜑𝜒→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2443, 2444
2446	→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒	Modus ponens 2436, 2445
2447	→→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2448	→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Modus ponens 2250, 2447
2449	→→↔𝜑𝜓→→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→→𝜓𝜑→𝜓𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒] into ax-2
2450	→→↔𝜑𝜓→→𝜑𝜒→→𝜓𝜑→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Modus ponens 2448, 2449
2451	→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒	Modus ponens 2446, 2450
2452	→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜑→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜑, 𝜒↗→→𝜑𝜒→𝜓𝜒] into ax-2
2453	→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜑→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Modus ponens 2451, 2452
2454	→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Modus ponens 2441, 2453
2455	→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2456	→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓	Modus ponens biimp, 2455
2457	→→↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
2458	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜑𝜓	Modus ponens 2456, 2457
2459	→→→𝜒𝜒→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2460	→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒	Modus ponens 51, 2459
2461	→→↔𝜑𝜓→→𝜒𝜒→𝜓→𝜒𝜒→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜓→𝜒𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
2462	→→↔𝜑𝜓→𝜒𝜒→↔𝜑𝜓→𝜓→𝜒𝜒	Modus ponens 2460, 2461
2463	→↔𝜑𝜓→𝜓→𝜒𝜒	Modus ponens 2426, 2462
2464	→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2465	→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Modus ponens 57, 2464
2466	→→↔𝜑𝜓→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→↔𝜑𝜓→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
2467	→→↔𝜑𝜓→𝜓→𝜒𝜒→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒	Modus ponens 2465, 2466
2468	→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒	Modus ponens 2463, 2467
2469	→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2470	→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 63, 2469
2471	→→↔𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
2472	→→↔𝜑𝜓→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 2470, 2471
2473	→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens biimp, 2472
2474	→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2475	→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 72, 2474
2476	→→↔𝜑𝜓→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒] into ax-2
2477	→→↔𝜑𝜓→→𝜓𝜒→𝜓𝜒→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 2475, 2476
2478	→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 2468, 2477
2479	→→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2480	→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 78, 2479
2481	→→↔𝜑𝜓→→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜒↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒] into ax-2
2482	→→↔𝜑𝜓→→𝜓𝜒→→𝜑𝜓→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 2480, 2481
2483	→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 2478, 2482
2484	→→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
2485	→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜓→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 2483, 2484
2486	→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 2473, 2485
2487	→→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2488	→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Modus ponens 2293, 2487
2489	→→↔𝜑𝜓→→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒] into ax-2
2490	→→↔𝜑𝜓→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Modus ponens 2488, 2489
2491	→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒	Modus ponens 2486, 2490
2492	→→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2493	→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Modus ponens 2300, 2492
2494	→→↔𝜑𝜓→→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒] into ax-2
2495	→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→→𝜓𝜒→𝜑𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Modus ponens 2493, 2494
2496	→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒	Modus ponens 2491, 2495
2497	→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2498	→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2499	→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Modus ponens 2497, 2498
2500	→→→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒] into ax-2
2501	→→→→𝜑𝜒→𝜓𝜒→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒	Modus ponens 2499, 2500
2502	→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2503	→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2496, 2502
2504	→→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗→→𝜑𝜒→𝜓𝜒] into ax-1
2505	→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2503, 2504
2506	→→→→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜓𝜒, 𝜓↗→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2
2507	→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2505, 2506
2508	→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2497, 2507
2509	→→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2510	→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2508, 2509
2511	→→↔𝜑𝜓→→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜓𝜒, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2
2512	→→↔𝜑𝜓→→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2510, 2511
2513	→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2454, 2512
2514	→→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔→𝜑𝜒→𝜓𝜒] into ax-2
2515	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2513, 2514
2516	→→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2517	→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2515, 2516
2518	→→↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒] into ax-2
2519	→→↔𝜑𝜓→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 2517, 2518
2520	→↔𝜑𝜓↔→𝜑𝜒→𝜓𝜒	Modus ponens 1651, 2515	imbi1
2521	→↔𝜑𝜓→𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into ax-1
2522	→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2523	→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓	Modus ponens 2521, 2522
2524	→→↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→𝜒↔𝜑𝜓] into ax-2
2525	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→𝜒↔𝜑𝜓	Modus ponens 2523, 2524
2526	↔→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74
2527	→↔→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Subs [𝜑↗→𝜒↔𝜑𝜓, 𝜓↗↔→𝜒𝜑→𝜒𝜓] into biimp
2528	→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Modus ponens 2526, 2527
2529	→→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Subs [𝜑↗→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
2530	→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Modus ponens 2528, 2529
2531	→→↔𝜑𝜓→→𝜒↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒↔𝜑𝜓, 𝜒↗↔→𝜒𝜑→𝜒𝜓] into ax-2
2532	→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Modus ponens 2530, 2531
2533	→↔𝜑𝜓↔→𝜒𝜑→𝜒𝜓	Modus ponens 2521, 2532	imbi2
2534	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into id
2535	→↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-1
2536	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 1927, 2535
2537	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74
2538	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp
2539	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Modus ponens 2537, 2538
2540	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Modus ponens 2534, 2539
2541	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74
2542	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp
2543	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2541, 2542
2544	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2536, 2543
2545	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into biimp
2546	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2544, 2545
2547	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp
2548	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Modus ponens 2540, 2547
2549	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into ax-1
2550	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2546, 2549
2551	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into ax-2
2552	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2550, 2551
2553	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2548, 2552
2554	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into bicom1
2555	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Modus ponens 2544, 2554
2556	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into biimp
2557	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑	Modus ponens 2555, 2556
2558	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑] into bicom1
2559	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Modus ponens 2540, 2558
2560	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into biimp
2561	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Modus ponens 2559, 2560
2562	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into ax-1
2563	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Modus ponens 2561, 2562
2564	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒] into ax-2
2565	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Modus ponens 2563, 2564
2566	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒	Modus ponens 2557, 2565
2567	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into impbi
2568	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2553, 2567
2569	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 2566, 2568
2570	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74
2571	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓] into bicom1
2572	↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Modus ponens 2570, 2571
2573	→↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp
2574	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Modus ponens 2572, 2573
2575	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Modus ponens 2569, 2574
2576	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into id
2577	→↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into ax-1
2578	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 1938, 2577
2579	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜓] into pm5.74
2580	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp
2581	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Modus ponens 2579, 2580
2582	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Modus ponens 2576, 2581
2583	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74
2584	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into biimp
2585	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2583, 2584
2586	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2578, 2585
2587	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into biimp
2588	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2586, 2587
2589	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp
2590	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Modus ponens 2582, 2589
2591	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into ax-1
2592	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2588, 2591
2593	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-2
2594	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2592, 2593
2595	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2590, 2594
2596	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into bicom1
2597	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Modus ponens 2586, 2596
2598	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into biimp
2599	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓	Modus ponens 2597, 2598
2600	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓] into bicom1
2601	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Modus ponens 2582, 2600
2602	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into biimp
2603	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Modus ponens 2601, 2602
2604	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Subs [𝜑↗→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into ax-1
2605	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Modus ponens 2603, 2604
2606	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓, 𝜒↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒] into ax-2
2607	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Modus ponens 2605, 2606
2608	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒	Modus ponens 2599, 2607
2609	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into impbi
2610	→→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2595, 2609
2611	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Modus ponens 2608, 2610
2612	↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓𝜒, 𝜒↗→↔𝜑𝜓𝜑] into pm5.74
2613	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑] into bicom1
2614	↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2612, 2613
2615	→↔↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑, 𝜓↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2616	→↔→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜒→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2614, 2615
2617	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2611, 2616
2618	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into impbi
2619	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Modus ponens 2575, 2618
2620	↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Modus ponens 2617, 2619
2621	↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into pm5.74
2622	↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into pm5.74
2623	→↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into bicom1
2624	↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2622, 2623
2625	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2626	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2624, 2625
2627	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp
2628	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-1
2629	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2626, 2628
2630	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
2631	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2629, 2630
2632	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2575, 2631
2633	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2634	→↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into biimp
2635	→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓	Modus ponens 2622, 2634
2636	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓] into bicom1
2637	↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2620, 2636
2638	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2639	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1
2640	→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2617, 2639
2641	→→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓, 𝜒↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into ax-2
2642	→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2640, 2641
2643	→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2635, 2642
2644	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi
2645	→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2632, 2644
2646	↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2643, 2645
2647	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2648	→↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2649	→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2621, 2648
2650	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into ax-1
2651	→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2632, 2650
2652	→→→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
2653	→→→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2651, 2652
2654	→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2649, 2653
2655	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2656	↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Modus ponens 2646, 2655
2657	→↔→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into biimp
2658	→↔→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑] into bicom1
2659	↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2621, 2658
2660	→↔↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp
2661	→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2659, 2660
2662	→→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1
2663	→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2661, 2662
2664	→→→↔𝜑𝜓↔𝜒𝜓→↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→↔𝜑𝜓↔𝜒𝜑→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜑] into ax-2
2665	→→→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓𝜒→↔𝜑𝜓𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2663, 2664
2666	→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2643, 2665
2667	→→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi
2668	→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2654, 2667
2669	↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2666, 2668
2670	↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜑, 𝜒↗↔𝜒𝜓] into pm5.74
2671	→↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓] into bicom1
2672	↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓	Modus ponens 2670, 2671
2673	→↔↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓	Subs [𝜑↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓] into biimp
2674	→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓	Modus ponens 2672, 2673
2675	→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓	Modus ponens 2669, 2674
2676	↔↔𝜑𝜒↔𝜒𝜑	Subs [𝜓↗𝜒] into bicom
2677	↔↔𝜓𝜒↔𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜒] into bicom
2678	→↔↔𝜑𝜒↔𝜒𝜑→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑	Subs [𝜑↗↔↔𝜑𝜒↔𝜒𝜑, 𝜓↗↔𝜑𝜓] into ax-1
2679	→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑	Modus ponens 2676, 2678
2680	↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜒𝜑] into pm5.74
2681	→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑] into biimp
2682	→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜑↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2680, 2681
2683	↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2679, 2682
2684	→↔→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓] into biimp
2685	→→↔𝜑𝜓↔↔𝜒𝜑↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2670, 2684
2686	→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2687	→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp
2688	→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2683, 2687
2689	→→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into ax-1
2690	→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2654, 2689
2691	→→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
2692	→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2690, 2691
2693	→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2688, 2692
2694	→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2695	↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑	Modus ponens 2669, 2694
2696	→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into biimp
2697	→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜑↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜑] into bicom1
2698	↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2683, 2697
2699	→↔→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜑, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into biimp
2700	→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2698, 2699
2701	→→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into ax-1
2702	→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2700, 2701
2703	→→→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜑→↔𝜑𝜓↔𝜑𝜒→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜑, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
2704	→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜑→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2702, 2703
2705	→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2666, 2704
2706	→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into impbi
2707	→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2693, 2706
2708	↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2705, 2707
2709	↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜒𝜓] into pm5.74
2710	→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓] into bicom1
2711	↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓	Modus ponens 2709, 2710
2712	→↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓	Subs [𝜑↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓] into biimp
2713	→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓	Modus ponens 2711, 2712
2714	→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓	Modus ponens 2708, 2713
2715	→↔↔𝜓𝜒↔𝜒𝜓↔↔𝜒𝜓↔𝜓𝜒	Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜒𝜓] into bicom1
2716	↔↔𝜒𝜓↔𝜓𝜒	Modus ponens 2677, 2715
2717	→↔↔𝜒𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒	Subs [𝜑↗↔↔𝜒𝜓↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2718	→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒	Modus ponens 2716, 2717
2719	→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓] into biimp
2720	→→↔𝜑𝜓↔↔𝜑𝜒↔𝜒𝜓↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2709, 2719
2721	↔→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗↔𝜓𝜒] into pm5.74
2722	→↔→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒, 𝜓↗↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒] into biimp
2723	→→↔𝜑𝜓↔↔𝜒𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2721, 2722
2724	↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2718, 2723
2725	→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into biimp
2726	→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2724, 2725
2727	→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2728	→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into ax-1
2729	→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2726, 2728
2730	→→→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2
2731	→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2729, 2730
2732	→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2693, 2731
2733	→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜓𝜒↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into bicom1
2734	↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2724, 2733
2735	→↔→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into biimp
2736	→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓	Modus ponens 2734, 2735
2737	→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒𝜓↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓] into bicom1
2738	↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2708, 2737
2739	→↔→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜑𝜒] into biimp
2740	→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into ax-1
2741	→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2705, 2740
2742	→→→↔𝜑𝜓↔𝜓𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
2743	→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜒𝜓→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2741, 2742
2744	→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2736, 2743
2745	→→→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒] into impbi
2746	→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2732, 2745
2747	↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 2744, 2746
2748	↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜓𝜒] into pm5.74
2749	→↔→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒] into bicom1
2750	↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒	Modus ponens 2748, 2749
2751	→↔↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒	Subs [𝜑↗↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒] into biimp
2752	→↔→↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒	Modus ponens 2750, 2751
2753	→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒	Modus ponens 2747, 2752	bibi1
2754	→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒	Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into biimp
2755	→→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒	Subs [𝜑↗→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
2756	→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒	Modus ponens 2754, 2755
2757	→→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜒↔𝜓𝜒→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜑𝜒↔𝜓𝜒, 𝜒↗→↔𝜑𝜒↔𝜓𝜒] into ax-2
2758	→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒	Modus ponens 2756, 2757
2759	→↔𝜑𝜓→↔𝜑𝜒↔𝜓𝜒	Modus ponens bibi1, 2758	bitr3
2760	↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓	Subs [𝜓↗¬𝜓] into notbi
2761	→↔¬𝜑𝜓↔¬𝜑𝜓	Subs [𝜑↗↔¬𝜑𝜓] into id
2762	→↔𝜓¬¬𝜓→↔¬𝜑𝜓↔𝜓¬¬𝜓	Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1
2763	→↔¬𝜑𝜓↔𝜓¬¬𝜓	Modus ponens 1915, 2762
2764	↔→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into pm5.74
2765	→↔→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓	Subs [𝜑↗→↔¬𝜑𝜓↔¬𝜑𝜓, 𝜓↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓] into biimp
2766	→→↔¬𝜑𝜓↔¬𝜑𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓	Modus ponens 2764, 2765
2767	↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓	Modus ponens 2761, 2766
2768	↔→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74
2769	→↔→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑𝜓↔𝜓¬¬𝜓, 𝜓↗↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓] into biimp
2770	→→↔¬𝜑𝜓↔𝜓¬¬𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2768, 2769
2771	↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2763, 2770
2772	→↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into biimp
2773	→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2771, 2772
2774	→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓	Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓] into biimp
2775	→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓	Modus ponens 2767, 2774
2776	→→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Subs [𝜑↗→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓¬𝜑] into ax-1
2777	→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2773, 2776
2778	→→→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓→→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓, 𝜒↗→↔¬𝜑𝜓¬¬𝜓] into ax-2
2779	→→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2777, 2778
2780	→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2775, 2779
2781	→↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬¬𝜓↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓	Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into bicom1
2782	↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓	Modus ponens 2771, 2781
2783	→↔→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓	Subs [𝜑↗→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓𝜓] into biimp
2784	→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓	Modus ponens 2782, 2783
2785	→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓𝜓↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓𝜓] into bicom1
2786	↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑	Modus ponens 2767, 2785
2787	→↔→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑𝜓𝜓, 𝜓↗→↔¬𝜑𝜓¬𝜑] into biimp
2788	→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑	Modus ponens 2786, 2787
2789	→→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑	Subs [𝜑↗→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into ax-1
2790	→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑	Modus ponens 2788, 2789
2791	→→→↔¬𝜑𝜓¬¬𝜓→→↔¬𝜑𝜓𝜓→↔¬𝜑𝜓¬𝜑→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓𝜓, 𝜒↗→↔¬𝜑𝜓¬𝜑] into ax-2
2792	→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓𝜓→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑	Modus ponens 2790, 2791
2793	→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑	Modus ponens 2784, 2792
2794	→→→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑𝜓¬𝜑, 𝜓↗→↔¬𝜑𝜓¬¬𝜓] into impbi
2795	→→→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓¬𝜑↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2780, 2794
2796	↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓	Modus ponens 2793, 2795
2797	↔→↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬¬𝜓] into pm5.74
2798	→↔→↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Subs [𝜑↗→↔¬𝜑𝜓↔¬𝜑¬¬𝜓, 𝜓↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓] into bicom1
2799	↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Modus ponens 2797, 2798
2800	→↔↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Subs [𝜑↗↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓, 𝜓↗→↔¬𝜑𝜓↔¬𝜑¬¬𝜓] into biimp
2801	→↔→↔¬𝜑𝜓¬𝜑→↔¬𝜑𝜓¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Modus ponens 2799, 2800
2802	→↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Modus ponens 2796, 2801
2803	→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓	Subs [𝜑↗↔¬𝜑¬¬𝜓] into id
2804	→↔𝜓¬¬𝜓↔¬¬𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗¬¬𝜓] into bicom1
2805	↔¬¬𝜓𝜓	Modus ponens 1915, 2804
2806	→↔¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓	Subs [𝜑↗↔¬¬𝜓𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into ax-1
2807	→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓	Modus ponens 2805, 2806
2808	↔→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓	Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬¬𝜓] into pm5.74
2809	→↔→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp
2810	→→↔¬𝜑¬¬𝜓↔¬𝜑¬¬𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓	Modus ponens 2808, 2809
2811	↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓	Modus ponens 2803, 2810
2812	↔→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗𝜓] into pm5.74
2813	→↔→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓] into biimp
2814	→→↔¬𝜑¬¬𝜓↔¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2812, 2813
2815	↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2807, 2814
2816	→↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into biimp
2817	→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2815, 2816
2818	→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp
2819	→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓	Modus ponens 2811, 2818
2820	→→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Subs [𝜑↗→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬𝜑] into ax-1
2821	→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2817, 2820
2822	→→→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓→→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜒↗→↔¬𝜑¬¬𝜓𝜓] into ax-2
2823	→→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2821, 2822
2824	→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2819, 2823
2825	→↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓𝜓↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into bicom1
2826	↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓	Modus ponens 2815, 2825
2827	→↔→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into biimp
2828	→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓	Modus ponens 2826, 2827
2829	→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓¬¬𝜓↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓] into bicom1
2830	↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑	Modus ponens 2811, 2829
2831	→↔→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬𝜑] into biimp
2832	→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑	Modus ponens 2830, 2831
2833	→→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑	Subs [𝜑↗→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into ax-1
2834	→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑	Modus ponens 2832, 2833
2835	→→→↔¬𝜑¬¬𝜓𝜓→→↔¬𝜑¬¬𝜓¬¬𝜓→↔¬𝜑¬¬𝜓¬𝜑→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓¬¬𝜓, 𝜒↗→↔¬𝜑¬¬𝜓¬𝜑] into ax-2
2836	→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬¬𝜓→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑	Modus ponens 2834, 2835
2837	→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑	Modus ponens 2828, 2836
2838	→→→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓¬𝜑, 𝜓↗→↔¬𝜑¬¬𝜓𝜓] into impbi
2839	→→→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓¬𝜑↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2824, 2838
2840	↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓	Modus ponens 2837, 2839
2841	↔→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓	Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗𝜓] into pm5.74
2842	→↔→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓, 𝜓↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓] into bicom1
2843	↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Modus ponens 2841, 2842
2844	→↔↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Subs [𝜑↗↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓, 𝜓↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓] into biimp
2845	→↔→↔¬𝜑¬¬𝜓¬𝜑→↔¬𝜑¬¬𝜓𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Modus ponens 2843, 2844
2846	→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Modus ponens 2840, 2845
2847	→→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into impbi
2848	→→↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Modus ponens 2802, 2847
2849	↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Modus ponens 2846, 2848
2850	↔↔¬𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗¬𝜑] into bicom
2851	→↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into bicom1
2852	↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Modus ponens 2849, 2851
2853	→↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into biimp
2854	→↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑¬¬𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into biimp
2855	→↔𝜑¬𝜓↔¬𝜑¬¬𝜓	Modus ponens 2760, 2854
2856	→→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓↔¬𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into ax-1
2857	→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓	Modus ponens 2846, 2856
2858	→→↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔¬𝜑𝜓→→↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓, 𝜒↗↔¬𝜑𝜓] into ax-2
2859	→→↔𝜑¬𝜓↔¬𝜑¬¬𝜓→↔𝜑¬𝜓↔¬𝜑𝜓	Modus ponens 2857, 2858
2860	→↔𝜑¬𝜓↔¬𝜑𝜓	Modus ponens 2855, 2859
2861	→↔↔¬𝜑¬¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔¬𝜑𝜓] into bicom1
2862	→↔↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔¬𝜑¬¬𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into biimp
2863	→↔↔𝜑¬𝜓↔¬𝜑¬¬𝜓↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑¬¬𝜓] into bicom1
2864	↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓	Modus ponens 2760, 2863
2865	→↔↔¬𝜑¬¬𝜓↔𝜑¬𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓	Subs [𝜑↗↔¬𝜑¬¬𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
2866	→↔¬𝜑¬¬𝜓↔𝜑¬𝜓	Modus ponens 2864, 2865
2867	→→↔¬𝜑¬¬𝜓↔𝜑¬𝜓→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓	Subs [𝜑↗→↔¬𝜑¬¬𝜓↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1
2868	→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓	Modus ponens 2866, 2867
2869	→→↔¬𝜑𝜓→↔¬𝜑¬¬𝜓↔𝜑¬𝜓→→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔¬𝜑¬¬𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2
2870	→→↔¬𝜑𝜓↔¬𝜑¬¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓	Modus ponens 2868, 2869
2871	→↔¬𝜑𝜓↔𝜑¬𝜓	Modus ponens 2802, 2870
2872	→→↔𝜑¬𝜓↔¬𝜑𝜓→→↔¬𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓↔¬𝜑𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into impbi
2873	→→↔¬𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓↔¬𝜑𝜓	Modus ponens 2860, 2872
2874	↔↔𝜑¬𝜓↔¬𝜑𝜓	Modus ponens 2871, 2873
2875	→↔↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into biimp
2876	→↔¬𝜑𝜓↔𝜓¬𝜑	Modus ponens 2850, 2875
2877	→↔↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔¬𝜑𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into biimp
2878	→→↔¬𝜑𝜓↔𝜓¬𝜑→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑𝜓↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓] into ax-1
2879	→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑	Modus ponens 2876, 2878
2880	→→↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜓¬𝜑→→↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓, 𝜒↗↔𝜓¬𝜑] into ax-2
2881	→→↔𝜑¬𝜓↔¬𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑	Modus ponens 2879, 2880
2882	→↔𝜑¬𝜓↔𝜓¬𝜑	Modus ponens 2860, 2881
2883	→↔↔¬𝜑𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑↔¬𝜑𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1
2884	↔↔𝜓¬𝜑↔¬𝜑𝜓	Modus ponens 2850, 2883
2885	→↔↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓	Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓] into biimp
2886	→↔𝜓¬𝜑↔¬𝜑𝜓	Modus ponens 2884, 2885
2887	→↔↔𝜑¬𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓↔𝜑¬𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔¬𝜑𝜓] into bicom1
2888	↔↔¬𝜑𝜓↔𝜑¬𝜓	Modus ponens 2874, 2887
2889	→↔↔¬𝜑𝜓↔𝜑¬𝜓→↔¬𝜑𝜓↔𝜑¬𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
2890	→→↔¬𝜑𝜓↔𝜑¬𝜓→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓	Subs [𝜑↗→↔¬𝜑𝜓↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into ax-1
2891	→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓	Modus ponens 2871, 2890
2892	→→↔𝜓¬𝜑→↔¬𝜑𝜓↔𝜑¬𝜓→→↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔𝜑¬𝜓	Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2
2893	→→↔𝜓¬𝜑↔¬𝜑𝜓→↔𝜓¬𝜑↔𝜑¬𝜓	Modus ponens 2891, 2892
2894	→↔𝜓¬𝜑↔𝜑¬𝜓	Modus ponens 2886, 2893
2895	→→↔𝜑¬𝜓↔𝜓¬𝜑→→↔𝜓¬𝜑↔𝜑¬𝜓↔↔𝜑¬𝜓↔𝜓¬𝜑	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into impbi
2896	→→↔𝜓¬𝜑↔𝜑¬𝜓↔↔𝜑¬𝜓↔𝜓¬𝜑	Modus ponens 2882, 2895
2897	↔↔𝜑¬𝜓↔𝜓¬𝜑	Modus ponens 2894, 2896	con2bi
2898	→→¬𝜓𝜑→¬𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into con1
2899	→→→¬𝜑𝜓→¬𝜓𝜑→→→¬𝜓𝜑→¬𝜑𝜓↔→¬𝜑𝜓→¬𝜓𝜑	Subs [𝜑↗→¬𝜑𝜓, 𝜓↗→¬𝜓𝜑] into impbi
2900	→→→¬𝜓𝜑→¬𝜑𝜓↔→¬𝜑𝜓→¬𝜓𝜑	Modus ponens con1, 2899
2901	↔→¬𝜑𝜓→¬𝜓𝜑	Modus ponens 2898, 2900	con1b
2902	→→𝜓¬𝜑→𝜑¬𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into con2
2903	→→→𝜑¬𝜓→𝜓¬𝜑→→→𝜓¬𝜑→𝜑¬𝜓↔→𝜑¬𝜓→𝜓¬𝜑	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜓¬𝜑] into impbi
2904	→→→𝜓¬𝜑→𝜑¬𝜓↔→𝜑¬𝜓→𝜓¬𝜑	Modus ponens con2, 2903
2905	↔→𝜑¬𝜓→𝜓¬𝜑	Modus ponens 2902, 2904	con2b
2906	→→𝜓→𝜑𝜓→𝜑→𝜓→𝜑𝜓	Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1
2907	→𝜑→𝜓→𝜑𝜓	Modus ponens 208, 2906
2908	→→→𝜑𝜓𝜓→→𝜓→𝜑𝜓↔→𝜑𝜓𝜓	Subs [𝜑↗→𝜑𝜓] into impbi
2909	→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1
2910	→→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1
2911	→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓	Modus ponens 2909, 2910
2912	→→𝜑→→𝜓→𝜑𝜓→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→𝜑→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓	Subs [𝜓↗→𝜓→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜓→𝜓→𝜑𝜓] into ax-2
2913	→→𝜑→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓	Modus ponens 2911, 2912
2914	→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓	Modus ponens 2907, 2913
2915	→→→→𝜑𝜓𝜓→→𝜓→𝜑𝜓↔→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓	Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→𝜓→𝜑𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2916	→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓	Modus ponens 2908, 2915
2917	→→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓	Subs [𝜑↗→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2918	→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓	Modus ponens 2916, 2917
2919	→→𝜑→→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓	Subs [𝜓↗→→→𝜑𝜓𝜓→𝜓→𝜑𝜓, 𝜒↗→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓] into ax-2
2920	→→𝜑→→→𝜑𝜓𝜓→𝜓→𝜑𝜓→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓	Modus ponens 2918, 2919
2921	→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓	Modus ponens 2914, 2920
2922	→→→𝜑𝜓𝜓→→𝜑𝜓𝜓	Subs [𝜑↗→→𝜑𝜓𝜓] into id
2923	→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2924	→→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1
2925	→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓	Modus ponens 2923, 2924
2926	→→→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓, 𝜒↗→𝜑→→𝜑𝜓𝜓] into ax-2
2927	→→→→𝜑𝜓𝜓→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓	Modus ponens 2925, 2926
2928	→→𝜑→→→𝜑𝜓𝜓↔→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2929	→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Modus ponens 2921, 2928
2930	→→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Subs [𝜑↗→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓, 𝜓↗→→𝜑𝜓𝜓] into ax-1
2931	→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Modus ponens 2929, 2930
2932	→→→→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Subs [𝜑↗→→𝜑𝜓𝜓, 𝜓↗→𝜑→→𝜑𝜓𝜓, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2
2933	→→→→𝜑𝜓𝜓→𝜑→→𝜑𝜓𝜓→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Modus ponens 2931, 2932
2934	→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Modus ponens 2923, 2933
2935	→→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Subs [𝜑↗→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2936	→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓	Modus ponens 2934, 2935
2937	→→𝜑→→→𝜑𝜓𝜓→𝜑↔→𝜑𝜓𝜓→→𝜑→→𝜑𝜓𝜓→𝜑→𝜑↔→𝜑𝜓𝜓	Subs [𝜓↗→→𝜑𝜓𝜓, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2
2938	→→𝜑→→𝜑𝜓𝜓→𝜑→𝜑↔→𝜑𝜓𝜓	Modus ponens 2936, 2937
2939	→𝜑→𝜑↔→𝜑𝜓𝜓	Modus ponens pm2.27, 2938
2940	→→𝜑→𝜑𝜑→𝜑→𝜑→𝜑𝜑	Subs [𝜑↗→𝜑→𝜑𝜑, 𝜓↗𝜑] into ax-1
2941	→𝜑→𝜑→𝜑𝜑	Modus ponens 5, 2940
2942	→→𝜑→𝜑→𝜑𝜑→→𝜑𝜑→𝜑→𝜑𝜑	Subs [𝜓↗𝜑, 𝜒↗→𝜑𝜑] into ax-2
2943	→→𝜑𝜑→𝜑→𝜑𝜑	Modus ponens 2941, 2942
2944	→→𝜑→𝜑↔→𝜑𝜓𝜓→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓	Subs [𝜓↗𝜑, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2945	→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓	Modus ponens 2939, 2944
2946	→→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓	Subs [𝜑↗→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2947	→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓	Modus ponens 2945, 2946
2948	→→𝜑→→𝜑𝜑→𝜑↔→𝜑𝜓𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜑𝜓𝜓	Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→𝜑𝜓𝜓] into ax-2
2949	→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜑𝜓𝜓	Modus ponens 2947, 2948
2950	→𝜑↔→𝜑𝜓𝜓	Modus ponens id, 2945	pm5.5
2951	↔↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓] into bicom
2952	→↔↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓𝜓, 𝜓↗↔𝜓→𝜑𝜓] into biimp
2953	→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓	Modus ponens 2951, 2952
2954	→→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓, 𝜓↗𝜑] into ax-1
2955	→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓	Modus ponens 2953, 2954
2956	→→𝜑→↔→𝜑𝜓𝜓↔𝜓→𝜑𝜓→→𝜑↔→𝜑𝜓𝜓→𝜑↔𝜓→𝜑𝜓	Subs [𝜓↗↔→𝜑𝜓𝜓, 𝜒↗↔𝜓→𝜑𝜓] into ax-2
2957	→→𝜑↔→𝜑𝜓𝜓→𝜑↔𝜓→𝜑𝜓	Modus ponens 2955, 2956
2958	→𝜑↔𝜓→𝜑𝜓	Modus ponens pm5.5, 2957	biimt
2959	↔↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓] into bicom
2960	→↔↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓	Subs [𝜑↗↔𝜓→𝜑𝜓, 𝜓↗↔→𝜑𝜓𝜓] into biimp
2961	→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓	Modus ponens 2959, 2960
2962	→→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓	Subs [𝜑↗→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
2963	→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓	Modus ponens 2961, 2962
2964	→→𝜑→↔𝜓→𝜑𝜓↔→𝜑𝜓𝜓→→𝜑↔𝜓→𝜑𝜓→𝜑↔→𝜑𝜓𝜓	Subs [𝜓↗↔𝜓→𝜑𝜓, 𝜒↗↔→𝜑𝜓𝜓] into ax-2
2965	→→𝜑↔𝜓→𝜑𝜓→𝜑↔→𝜑𝜓𝜓	Modus ponens 2963, 2964
2966	→¬𝜑↔¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into biimt
2967	↔→𝜓𝜑→¬𝜑¬𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into con34b
2968	→↔→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→¬𝜑¬𝜓] into bicom1
2969	↔→¬𝜑¬𝜓→𝜓𝜑	Modus ponens 2967, 2968
2970	→↔→¬𝜑¬𝜓→𝜓𝜑→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑	Subs [𝜑↗↔→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗¬𝜑] into ax-1
2971	→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑	Modus ponens 2969, 2970
2972	↔→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗→¬𝜑¬𝜓] into pm5.74
2973	→↔→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓] into biimp
2974	→→¬𝜑↔¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓	Modus ponens 2972, 2973
2975	↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓	Modus ponens 2966, 2974
2976	↔→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→𝜓𝜑] into pm5.74
2977	→↔→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Subs [𝜑↗→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑, 𝜓↗↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑] into biimp
2978	→→¬𝜑↔→¬𝜑¬𝜓→𝜓𝜑↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 2976, 2977
2979	↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 2971, 2978
2980	→↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into biimp
2981	→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 2979, 2980
2982	→↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into biimp
2983	→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓	Modus ponens 2975, 2982
2984	→→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Subs [𝜑↗→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑¬𝜓] into ax-1
2985	→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 2981, 2984
2986	→→→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓, 𝜒↗→¬𝜑→𝜓𝜑] into ax-2
2987	→→→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 2985, 2986
2988	→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 2983, 2987
2989	→↔→¬𝜑→¬𝜑¬𝜓→¬𝜑→𝜓𝜑↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into bicom1
2990	↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓	Modus ponens 2979, 2989
2991	→↔→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into biimp
2992	→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓	Modus ponens 2990, 2991
2993	→↔→¬𝜑¬𝜓→¬𝜑→¬𝜑¬𝜓↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→¬𝜑¬𝜓] into bicom1
2994	↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 2975, 2993
2995	→↔→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
2996	→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 2994, 2995
2997	→→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into ax-1
2998	→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 2996, 2997
2999	→→→¬𝜑→𝜓𝜑→→¬𝜑→¬𝜑¬𝜓→¬𝜑¬𝜓→→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑→¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
3000	→→→¬𝜑→𝜓𝜑→¬𝜑→¬𝜑¬𝜓→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓	Modus ponens 2998, 2999
3001	→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓	Modus ponens 2992, 3000
3002	→→→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑→𝜓𝜑] into impbi
3003	→→→¬𝜑→𝜓𝜑→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 2988, 3002
3004	↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Modus ponens 3001, 3003
3005	↔→¬𝜑↔¬𝜓→𝜓𝜑↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗→𝜓𝜑] into pm5.74
3006	→↔→¬𝜑↔¬𝜓→𝜓𝜑↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑	Subs [𝜑↗→¬𝜑↔¬𝜓→𝜓𝜑, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑] into bicom1
3007	↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑	Modus ponens 3005, 3006
3008	→↔↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑→↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑	Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑, 𝜓↗→¬𝜑↔¬𝜓→𝜓𝜑] into biimp
3009	→↔→¬𝜑¬𝜓→¬𝜑→𝜓𝜑→¬𝜑↔¬𝜓→𝜓𝜑	Modus ponens 3007, 3008
3010	→¬𝜑↔¬𝜓→𝜓𝜑	Modus ponens 3004, 3009	mtt
3011	→¬𝜓↔¬𝜑→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into mtt
3012	↔↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑𝜓] into bicom
3013	→↔↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑	Subs [𝜑↗↔¬𝜑→𝜑𝜓, 𝜓↗↔→𝜑𝜓¬𝜑] into biimp
3014	→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑	Modus ponens 3012, 3013
3015	→→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
3016	→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑	Modus ponens 3014, 3015
3017	→→¬𝜓→↔¬𝜑→𝜑𝜓↔→𝜑𝜓¬𝜑→→¬𝜓↔¬𝜑→𝜑𝜓→¬𝜓↔→𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑→𝜑𝜓, 𝜒↗↔→𝜑𝜓¬𝜑] into ax-2
3018	→→¬𝜓↔¬𝜑→𝜑𝜓→¬𝜓↔→𝜑𝜓¬𝜑	Modus ponens 3016, 3017
3019	→¬𝜓↔→𝜑𝜓¬𝜑	Modus ponens 3011, 3018	imnot
3020	→𝜑→↔𝜑𝜓𝜑	Subs [𝜓↗↔𝜑𝜓] into ax-1
3021	→→𝜑→↔𝜑𝜓𝜑→𝜑→𝜑→↔𝜑𝜓𝜑	Subs [𝜑↗→𝜑→↔𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
3022	→𝜑→𝜑→↔𝜑𝜓𝜑	Modus ponens 3020, 3021
3023	→→𝜑→𝜑→↔𝜑𝜓𝜑→→𝜑𝜑→𝜑→↔𝜑𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗→↔𝜑𝜓𝜑] into ax-2
3024	→→𝜑𝜑→𝜑→↔𝜑𝜓𝜑	Modus ponens 3022, 3023
3025	→→↔𝜑𝜓→𝜑𝜓→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
3026	→→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Subs [𝜑↗→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
3027	→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓	Modus ponens 1929, 3026
3028	→→𝜑→→↔𝜑𝜓𝜑→↔𝜑𝜓𝜓→→𝜑→↔𝜑𝜓𝜑→𝜑→↔𝜑𝜓𝜓	Subs [𝜓↗→↔𝜑𝜓𝜑, 𝜒↗→↔𝜑𝜓𝜓] into ax-2
3029	→→𝜑→↔𝜑𝜓𝜑→𝜑→↔𝜑𝜓𝜓	Modus ponens 3027, 3028
3030	→𝜑→↔𝜑𝜓𝜓	Modus ponens 3020, 3029
3031	→→𝜓↔𝜑𝜓→→↔𝜑𝜓𝜓↔𝜓↔𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into impbi
3032	→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1
3033	→→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓	Subs [𝜑↗→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
3034	→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓	Modus ponens 3032, 3033
3035	→→𝜑→→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜑→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓	Subs [𝜓↗→↔𝜑𝜓𝜓, 𝜒↗→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓] into ax-2
3036	→→𝜑→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓	Modus ponens 3034, 3035
3037	→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓	Modus ponens 3030, 3036
3038	→→→𝜓↔𝜑𝜓→→↔𝜑𝜓𝜓↔𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓	Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→↔𝜑𝜓𝜓, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2
3039	→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓	Modus ponens 3031, 3038
3040	→→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓	Subs [𝜑↗→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3041	→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓	Modus ponens 3039, 3040
3042	→→𝜑→→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓	Subs [𝜓↗→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓, 𝜒↗→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓] into ax-2
3043	→→𝜑→→𝜓↔𝜑𝜓→↔𝜑𝜓𝜓→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓	Modus ponens 3041, 3042
3044	→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓	Modus ponens 3037, 3043
3045	→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓	Subs [𝜑↗→𝜓↔𝜑𝜓] into id
3046	→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓	Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3047	→→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓	Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1
3048	→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓	Modus ponens 3046, 3047
3049	→→→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓	Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜑→𝜓↔𝜑𝜓] into ax-2
3050	→→→𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓	Modus ponens 3048, 3049
3051	→→𝜑→→𝜓↔𝜑𝜓↔𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Subs [𝜓↗→𝜓↔𝜑𝜓, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2
3052	→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3044, 3051
3053	→→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Subs [𝜑↗→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓, 𝜓↗→𝜓↔𝜑𝜓] into ax-1
3054	→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3052, 3053
3055	→→→𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Subs [𝜑↗→𝜓↔𝜑𝜓, 𝜓↗→𝜑→𝜓↔𝜑𝜓, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2
3056	→→→𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3054, 3055
3057	→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3046, 3056
3058	→→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Subs [𝜑↗→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3059	→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3057, 3058
3060	→→𝜑→→𝜓↔𝜑𝜓→𝜑↔𝜓↔𝜑𝜓→→𝜑→𝜓↔𝜑𝜓→𝜑→𝜑↔𝜓↔𝜑𝜓	Subs [𝜓↗→𝜓↔𝜑𝜓, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2
3061	→→𝜑→𝜓↔𝜑𝜓→𝜑→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3059, 3060
3062	→𝜑→𝜑↔𝜓↔𝜑𝜓	Modus ponens pm5.1im, 3061
3063	→→𝜑→𝜑↔𝜓↔𝜑𝜓→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓	Subs [𝜓↗𝜑, 𝜒↗↔𝜓↔𝜑𝜓] into ax-2
3064	→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3062, 3063
3065	→→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓	Subs [𝜑↗→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
3066	→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3064, 3065
3067	→→𝜑→→𝜑𝜑→𝜑↔𝜓↔𝜑𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓↔𝜑𝜓	Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔𝜓↔𝜑𝜓] into ax-2
3068	→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓↔𝜑𝜓	Modus ponens 3066, 3067
3069	→𝜑↔𝜓↔𝜑𝜓	Modus ponens id, 3064	pm5.501
3070	↔→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜒↗↔𝜑𝜓] into pm5.74
3071	→↔→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3072	→→𝜑↔𝜓↔𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3070, 3071
3073	↔→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens pm5.501, 3072	ibib
3074	→↔↔𝜑𝜓↔𝜓𝜑→𝜑↔↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗𝜑] into ax-1
3075	→𝜑↔↔𝜑𝜓↔𝜓𝜑	Modus ponens bicom, 3074
3076	↔→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into pm5.74
3077	→↔→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜑↗→𝜑↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑] into biimp
3078	→→𝜑↔↔𝜑𝜓↔𝜓𝜑↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3076, 3077
3079	↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3075, 3078
3080	→↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into biimp
3081	→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3079, 3080
3082	→↔→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓] into biimp
3083	→→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜑↗→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
3084	→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3081, 3083
3085	→→→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑→→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑↔𝜓𝜑] into ax-2
3086	→→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3084, 3085
3087	→→𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 1697, 3086
3088	→↔→𝜑↔𝜑𝜓→𝜑↔𝜓𝜑↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into bicom1
3089	↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓	Modus ponens 3079, 3088
3090	→↔→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜑𝜓] into biimp
3091	→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓	Modus ponens 3089, 3090
3092	→↔→𝜑𝜓→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓] into bicom1
3093	↔→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens ibib, 3092
3094	→↔→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
3095	→→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3093, 3094
3096	→→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into ax-1
3097	→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3095, 3096
3098	→→→𝜑↔𝜓𝜑→→𝜑↔𝜑𝜓→𝜑𝜓→→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
3099	→→→𝜑↔𝜓𝜑→𝜑↔𝜑𝜓→→𝜑↔𝜓𝜑→𝜑𝜓	Modus ponens 3097, 3098
3100	→→𝜑↔𝜓𝜑→𝜑𝜓	Modus ponens 3091, 3099
3101	→→→𝜑𝜓→𝜑↔𝜓𝜑→→→𝜑↔𝜓𝜑→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜑] into impbi
3102	→→→𝜑↔𝜓𝜑→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3087, 3101
3103	↔→𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3100, 3102	ibibr
3104	↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜒↗↔𝜓𝜑] into pm5.74
3105	→↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑	Subs [𝜑↗→𝜑↔𝜓↔𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑↔𝜓𝜑] into bicom1
3106	↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑	Modus ponens 3104, 3105
3107	→↔↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑→↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜑↔𝜓𝜑, 𝜓↗→𝜑↔𝜓↔𝜓𝜑] into biimp
3108	→↔→𝜑𝜓→𝜑↔𝜓𝜑→𝜑↔𝜓↔𝜓𝜑	Modus ponens 3106, 3107
3109	→𝜑↔𝜓↔𝜓𝜑	Modus ponens ibibr, 3108
3110	→↔→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑→→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑	Subs [𝜑↗→𝜑↔𝜓↔𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑↔𝜓𝜑] into biimp
3111	→→𝜑↔𝜓↔𝜓𝜑↔→𝜑𝜓→𝜑↔𝜓𝜑	Modus ponens 3104, 3110
3112	→¬𝜑↔¬𝜓↔¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into pm5.501
3113	→↔↔𝜑𝜓↔¬𝜑¬𝜓↔↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔¬𝜑¬𝜓] into bicom1
3114	↔↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens notbi, 3113
3115	→↔↔¬𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
3116	→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 3114, 3115
3117	↔→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔¬𝜑¬𝜓] into pm5.74
3118	→↔→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓↔¬𝜑¬𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓] into biimp
3119	→→¬𝜑↔¬𝜓↔¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓	Modus ponens 3117, 3118
3120	↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓	Modus ponens 3112, 3119
3121	↔→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3122	→↔→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3123	→→¬𝜑↔↔¬𝜑¬𝜓↔𝜑𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3121, 3122
3124	↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3116, 3123
3125	→↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into biimp
3126	→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3124, 3125
3127	→↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into biimp
3128	→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓	Modus ponens 3120, 3127
3129	→→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓] into ax-1
3130	→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3126, 3129
3131	→→→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2
3132	→→→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3130, 3131
3133	→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3128, 3132
3134	→↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into bicom1
3135	↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓	Modus ponens 3124, 3134
3136	→↔→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into biimp
3137	→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓	Modus ponens 3135, 3136
3138	→↔→¬𝜑¬𝜓→¬𝜑↔¬𝜑¬𝜓↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓] into bicom1
3139	↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3120, 3138
3140	→↔→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
3141	→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3139, 3140
3142	→→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into ax-1
3143	→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3141, 3142
3144	→→→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜑¬𝜓→¬𝜑¬𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜑¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
3145	→→→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3143, 3144
3146	→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3137, 3145
3147	→→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into impbi
3148	→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3133, 3147
3149	↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3146, 3148
3150	↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3151	→↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3152	↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓	Modus ponens 3150, 3151
3153	→↔↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓↔𝜑𝜓] into biimp
3154	→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬𝜓↔𝜑𝜓	Modus ponens 3152, 3153
3155	→¬𝜑↔¬𝜓↔𝜑𝜓	Modus ponens 3149, 3154	nbn2
3156	→¬𝜓↔¬𝜑↔𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗𝜑] into nbn2
3157	↔↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into bicom
3158	→↔↔𝜓𝜑↔𝜑𝜓→¬𝜓↔↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗¬𝜓] into ax-1
3159	→¬𝜓↔↔𝜓𝜑↔𝜑𝜓	Modus ponens 3157, 3158
3160	↔→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜓𝜑] into pm5.74
3161	→↔→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑	Subs [𝜑↗→¬𝜓↔¬𝜑↔𝜓𝜑, 𝜓↗↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑] into biimp
3162	→→¬𝜓↔¬𝜑↔𝜓𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑	Modus ponens 3160, 3161
3163	↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑	Modus ponens 3156, 3162
3164	↔→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗↔𝜓𝜑, 𝜒↗↔𝜑𝜓] into pm5.74
3165	→↔→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬𝜓↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓] into biimp
3166	→→¬𝜓↔↔𝜓𝜑↔𝜑𝜓↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3164, 3165
3167	↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3159, 3166
3168	→↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into biimp
3169	→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3167, 3168
3170	→↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑	Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑] into biimp
3171	→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑	Modus ponens 3163, 3170
3172	→→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓¬𝜑] into ax-1
3173	→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3169, 3172
3174	→→→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓→→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑, 𝜒↗→¬𝜓↔𝜑𝜓] into ax-2
3175	→→→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3173, 3174
3176	→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3171, 3175
3177	→↔→¬𝜓↔𝜓𝜑→¬𝜓↔𝜑𝜓↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑	Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into bicom1
3178	↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑	Modus ponens 3167, 3177
3179	→↔→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑	Subs [𝜑↗→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔𝜓𝜑] into biimp
3180	→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑	Modus ponens 3178, 3179
3181	→↔→¬𝜓¬𝜑→¬𝜓↔𝜓𝜑↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑	Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜓𝜑] into bicom1
3182	↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑	Modus ponens 3163, 3181
3183	→↔→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑	Subs [𝜑↗→¬𝜓↔𝜓𝜑, 𝜓↗→¬𝜓¬𝜑] into biimp
3184	→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑	Modus ponens 3182, 3183
3185	→→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑	Subs [𝜑↗→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into ax-1
3186	→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑	Modus ponens 3184, 3185
3187	→→→¬𝜓↔𝜑𝜓→→¬𝜓↔𝜓𝜑→¬𝜓¬𝜑→→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑	Subs [𝜑↗→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔𝜓𝜑, 𝜒↗→¬𝜓¬𝜑] into ax-2
3188	→→→¬𝜓↔𝜑𝜓→¬𝜓↔𝜓𝜑→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑	Modus ponens 3186, 3187
3189	→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑	Modus ponens 3180, 3188
3190	→→→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬𝜓¬𝜑, 𝜓↗→¬𝜓↔𝜑𝜓] into impbi
3191	→→→¬𝜓↔𝜑𝜓→¬𝜓¬𝜑↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3176, 3190
3192	↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3189, 3191
3193	↔→¬𝜓↔¬𝜑↔𝜑𝜓↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜑𝜓] into pm5.74
3194	→↔→¬𝜓↔¬𝜑↔𝜑𝜓↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜓↔¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓] into bicom1
3195	↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓	Modus ponens 3193, 3194
3196	→↔↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓→↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓, 𝜓↗→¬𝜓↔¬𝜑↔𝜑𝜓] into biimp
3197	→↔→¬𝜓¬𝜑→¬𝜓↔𝜑𝜓→¬𝜓↔¬𝜑↔𝜑𝜓	Modus ponens 3195, 3196
3198	→¬𝜓↔¬𝜑↔𝜑𝜓	Modus ponens 3192, 3197
3199	↔↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗↔𝜑𝜓] into bicom
3200	→↔↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑	Subs [𝜑↗↔¬𝜑↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬𝜑] into biimp
3201	→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑	Modus ponens 3199, 3200
3202	→→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑	Subs [𝜑↗→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
3203	→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑	Modus ponens 3201, 3202
3204	→→¬𝜓→↔¬𝜑↔𝜑𝜓↔↔𝜑𝜓¬𝜑→→¬𝜓↔¬𝜑↔𝜑𝜓→¬𝜓↔↔𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗↔¬𝜑↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬𝜑] into ax-2
3205	→→¬𝜓↔¬𝜑↔𝜑𝜓→¬𝜓↔↔𝜑𝜓¬𝜑	Modus ponens 3203, 3204
3206	→¬𝜓↔↔𝜑𝜓¬𝜑	Modus ponens 3198, 3205	bibif
3207	→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑𝜓] into biimp
3208	→→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓	Subs [𝜑↗→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
3209	→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓	Modus ponens 3207, 3208
3210	→→¬𝜑→↔¬𝜓↔𝜑𝜓→¬𝜓↔𝜑𝜓→→¬𝜑↔¬𝜓↔𝜑𝜓→¬𝜑→¬𝜓↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓↔𝜑𝜓, 𝜒↗→¬𝜓↔𝜑𝜓] into ax-2
3211	→→¬𝜑↔¬𝜓↔𝜑𝜓→¬𝜑→¬𝜓↔𝜑𝜓	Modus ponens 3209, 3210
3212	→¬𝜑→¬𝜓↔𝜑𝜓	Modus ponens nbn2, 3211	pm5.21im
3213	→𝜑↔¬𝜓↔𝜑¬𝜓	Subs [𝜓↗¬𝜓] into pm5.501
3214	↔↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑¬𝜓] into bicom
3215	→↔↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓	Subs [𝜑↗↔¬𝜓↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬𝜓] into biimp
3216	→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓	Modus ponens 3214, 3215
3217	→→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓	Subs [𝜑↗→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓, 𝜓↗𝜑] into ax-1
3218	→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓	Modus ponens 3216, 3217
3219	→→𝜑→↔¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓→→𝜑↔¬𝜓↔𝜑¬𝜓→𝜑↔↔𝜑¬𝜓¬𝜓	Subs [𝜓↗↔¬𝜓↔𝜑¬𝜓, 𝜒↗↔↔𝜑¬𝜓¬𝜓] into ax-2
3220	→→𝜑↔¬𝜓↔𝜑¬𝜓→𝜑↔↔𝜑¬𝜓¬𝜓	Modus ponens 3218, 3219
3221	→𝜑↔↔𝜑¬𝜓¬𝜓	Modus ponens 3213, 3220
3222	↔↔𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓	Subs [𝜑↗𝜓, 𝜓↗↔𝜑¬𝜓] into con2bi
3223	→↔↔𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬𝜓↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓	Subs [𝜑↗↔𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬𝜓] into bicom1
3224	↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓	Modus ponens 3222, 3223
3225	→↔↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓	Subs [𝜑↗↔↔𝜑¬𝜓¬𝜓, 𝜓↗↔𝜓¬↔𝜑¬𝜓] into biimp
3226	→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓	Modus ponens 3224, 3225
3227	→→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑] into ax-1
3228	→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓	Modus ponens 3226, 3227
3229	→→𝜑→↔↔𝜑¬𝜓¬𝜓↔𝜓¬↔𝜑¬𝜓→→𝜑↔↔𝜑¬𝜓¬𝜓→𝜑↔𝜓¬↔𝜑¬𝜓	Subs [𝜓↗↔↔𝜑¬𝜓¬𝜓, 𝜒↗↔𝜓¬↔𝜑¬𝜓] into ax-2
3230	→→𝜑↔↔𝜑¬𝜓¬𝜓→𝜑↔𝜓¬↔𝜑¬𝜓	Modus ponens 3228, 3229
3231	→𝜑↔𝜓¬↔𝜑¬𝜓	Modus ponens 3221, 3230
3232	↔↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom
3233	→↔↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓	Subs [𝜑↗↔𝜓¬↔𝜑¬𝜓, 𝜓↗↔¬↔𝜑¬𝜓𝜓] into biimp
3234	→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓	Modus ponens 3232, 3233
3235	→→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓	Subs [𝜑↗→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓, 𝜓↗𝜑] into ax-1
3236	→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓	Modus ponens 3234, 3235
3237	→→𝜑→↔𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓𝜓→→𝜑↔𝜓¬↔𝜑¬𝜓→𝜑↔¬↔𝜑¬𝜓𝜓	Subs [𝜓↗↔𝜓¬↔𝜑¬𝜓, 𝜒↗↔¬↔𝜑¬𝜓𝜓] into ax-2
3238	→→𝜑↔𝜓¬↔𝜑¬𝜓→𝜑↔¬↔𝜑¬𝜓𝜓	Modus ponens 3236, 3237
3239	→𝜑↔¬↔𝜑¬𝜓𝜓	Modus ponens 3231, 3238
3240	↔→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓	Subs [𝜓↗¬↔𝜑¬𝜓, 𝜒↗𝜓] into pm5.74
3241	→↔→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑↔¬↔𝜑¬𝜓𝜓, 𝜓↗↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓] into biimp
3242	→→𝜑↔¬↔𝜑¬𝜓𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓	Modus ponens 3240, 3241
3243	↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓	Modus ponens 3239, 3242
3244	→↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓] into biimp
3245	→→𝜑¬↔𝜑¬𝜓→𝜑𝜓	Modus ponens 3243, 3244
3246	→→→𝜑𝜓→𝜑↔𝜑𝜓→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑¬↔𝜑¬𝜓] into ax-1
3247	→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 1697, 3246
3248	→→→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
3249	→→→𝜑¬↔𝜑¬𝜓→𝜑𝜓→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓	Modus ponens 3247, 3248
3250	→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓	Modus ponens 3245, 3249
3251	→↔→𝜑¬↔𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑𝜓] into bicom1
3252	↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓	Modus ponens 3243, 3251
3253	→↔→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬↔𝜑¬𝜓] into biimp
3254	→→𝜑𝜓→𝜑¬↔𝜑¬𝜓	Modus ponens 3252, 3253
3255	→→→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑↔𝜑𝜓] into ax-1
3256	→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓	Modus ponens 3254, 3255
3257	→→→𝜑↔𝜑𝜓→→𝜑𝜓→𝜑¬↔𝜑¬𝜓→→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬↔𝜑¬𝜓] into ax-2
3258	→→→𝜑↔𝜑𝜓→𝜑𝜓→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓	Modus ponens 3256, 3257
3259	→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓	Modus ponens 3095, 3258
3260	→→→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑¬↔𝜑¬𝜓, 𝜓↗→𝜑↔𝜑𝜓] into impbi
3261	→→→𝜑↔𝜑𝜓→𝜑¬↔𝜑¬𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓	Modus ponens 3250, 3260
3262	↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓	Modus ponens 3259, 3261
3263	↔→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓	Subs [𝜓↗¬↔𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3264	→↔→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓] into bicom1
3265	↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Modus ponens 3263, 3264
3266	→↔↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓] into biimp
3267	→↔→𝜑¬↔𝜑¬𝜓→𝜑↔𝜑𝜓→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Modus ponens 3265, 3266
3268	→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Modus ponens 3262, 3267
3269	↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬↔𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into bicom
3270	→↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into biimp
3271	→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3269, 3270
3272	→→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑] into ax-1
3273	→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3271, 3272
3274	→→𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜓↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3275	→→𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3273, 3274
3276	→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3268, 3275
3277	→¬𝜑↔¬¬𝜓↔𝜑¬𝜓	Subs [𝜓↗¬𝜓] into nbn2
3278	↔↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑¬𝜓] into bicom
3279	→↔↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓	Subs [𝜑↗↔¬¬𝜓↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓] into biimp
3280	→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓	Modus ponens 3278, 3279
3281	→→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓	Subs [𝜑↗→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1
3282	→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓	Modus ponens 3280, 3281
3283	→→¬𝜑→↔¬¬𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓→→¬𝜑↔¬¬𝜓↔𝜑¬𝜓→¬𝜑↔↔𝜑¬𝜓¬¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔¬¬𝜓↔𝜑¬𝜓, 𝜒↗↔↔𝜑¬𝜓¬¬𝜓] into ax-2
3284	→→¬𝜑↔¬¬𝜓↔𝜑¬𝜓→¬𝜑↔↔𝜑¬𝜓¬¬𝜓	Modus ponens 3282, 3283
3285	→¬𝜑↔↔𝜑¬𝜓¬¬𝜓	Modus ponens 3277, 3284
3286	↔↔¬𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗↔𝜑¬𝜓] into con2bi
3287	→↔↔¬𝜓¬↔𝜑¬𝜓↔↔𝜑¬𝜓¬¬𝜓↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓	Subs [𝜑↗↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓] into bicom1
3288	↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓	Modus ponens 3286, 3287
3289	→↔↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓	Subs [𝜑↗↔↔𝜑¬𝜓¬¬𝜓, 𝜓↗↔¬𝜓¬↔𝜑¬𝜓] into biimp
3290	→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓	Modus ponens 3288, 3289
3291	→→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3292	→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓	Modus ponens 3290, 3291
3293	→→¬𝜑→↔↔𝜑¬𝜓¬¬𝜓↔¬𝜓¬↔𝜑¬𝜓→→¬𝜑↔↔𝜑¬𝜓¬¬𝜓→¬𝜑↔¬𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑¬𝜓¬¬𝜓, 𝜒↗↔¬𝜓¬↔𝜑¬𝜓] into ax-2
3294	→→¬𝜑↔↔𝜑¬𝜓¬¬𝜓→¬𝜑↔¬𝜓¬↔𝜑¬𝜓	Modus ponens 3292, 3293
3295	→¬𝜑↔¬𝜓¬↔𝜑¬𝜓	Modus ponens 3285, 3294
3296	↔↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom
3297	→↔↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓	Subs [𝜑↗↔¬𝜓¬↔𝜑¬𝜓, 𝜓↗↔¬↔𝜑¬𝜓¬𝜓] into biimp
3298	→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓	Modus ponens 3296, 3297
3299	→→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓	Subs [𝜑↗→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓, 𝜓↗¬𝜑] into ax-1
3300	→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓	Modus ponens 3298, 3299
3301	→→¬𝜑→↔¬𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓¬𝜓→→¬𝜑↔¬𝜓¬↔𝜑¬𝜓→¬𝜑↔¬↔𝜑¬𝜓¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓¬↔𝜑¬𝜓, 𝜒↗↔¬↔𝜑¬𝜓¬𝜓] into ax-2
3302	→→¬𝜑↔¬𝜓¬↔𝜑¬𝜓→¬𝜑↔¬↔𝜑¬𝜓¬𝜓	Modus ponens 3300, 3301
3303	→¬𝜑↔¬↔𝜑¬𝜓¬𝜓	Modus ponens 3295, 3302
3304	↔→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑¬𝜓, 𝜒↗¬𝜓] into pm5.74
3305	→↔→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔¬↔𝜑¬𝜓¬𝜓, 𝜓↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3306	→→¬𝜑↔¬↔𝜑¬𝜓¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3304, 3305
3307	↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3303, 3306
3308	→↔→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3309	→→¬𝜑↔¬𝜓↔𝜑𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3150, 3308
3310	→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into biimp
3311	→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
3312	→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3307, 3311
3313	→→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬↔𝜑¬𝜓] into ax-1
3314	→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3133, 3313
3315	→→→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2
3316	→→→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3314, 3315
3317	→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3312, 3316
3318	→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into bicom1
3319	↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3149, 3318
3320	→↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓] into biimp
3321	→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓] into bicom1
3322	↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓	Modus ponens 3307, 3321
3323	→↔→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬↔𝜑¬𝜓] into biimp
3324	→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓	Modus ponens 3322, 3323
3325	→→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into ax-1
3326	→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓	Modus ponens 3324, 3325
3327	→→→¬𝜑↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑¬↔𝜑¬𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑¬↔𝜑¬𝜓] into ax-2
3328	→→→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓	Modus ponens 3326, 3327
3329	→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓	Modus ponens 3146, 3328
3330	→→→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑¬↔𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜑𝜓] into impbi
3331	→→→¬𝜑↔𝜑𝜓→¬𝜑¬↔𝜑¬𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3317, 3330
3332	↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3329, 3331
3333	↔→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into pm5.74
3334	→↔→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3335	↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Modus ponens 3333, 3334
3336	→↔↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓] into biimp
3337	→↔→¬𝜑¬↔𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Modus ponens 3335, 3336
3338	→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓	Modus ponens 3332, 3337
3339	→→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3340	→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3271, 3339
3341	→→¬𝜑→↔¬↔𝜑¬𝜓↔𝜑𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3342	→→¬𝜑↔¬↔𝜑¬𝜓↔𝜑𝜓→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3340, 3341
3343	→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3338, 3342
3344	→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into id
3345	→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3346	→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3344, 3345
3347	→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into notnotr
3348	→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3349	→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3350	→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3348, 3349
3351	→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3352	→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3350, 3351
3353	→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3347, 3352
3354	→→¬𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3355	→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3346, 3354
3356	→→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3357	→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3355, 3356
3358	→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3359	→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3357, 3358
3360	→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3361	→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
3362	→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑	Modus ponens 3360, 3361
3363	→→¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑] into ax-2
3364	→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑	Modus ponens 3362, 3363
3365	→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3366	→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3353, 3365
3367	→→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3368	→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3366, 3367
3369	→→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑, 𝜒↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3370	→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3368, 3369
3371	→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3360, 3370
3372	→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-3
3373	→→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
3374	→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3372, 3373
3375	→→¬𝜑→→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3376	→→¬𝜑→¬¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3374, 3375
3377	→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3371, 3376
3378	→→¬𝜑→↔↔𝜑𝜓¬↔𝜑¬𝜓¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜒↗¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3379	→→¬𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3377, 3378
3380	→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3343, 3379
3381	→→¬𝜑¬¬↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑	Subs [𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-3
3382	→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑	Modus ponens 3380, 3381
3383	→→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-1
3384	→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3276, 3383
3385	→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓→𝜑↔↔𝜑𝜓¬↔𝜑¬𝜓→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗¬↔↔𝜑𝜓¬↔𝜑¬𝜓, 𝜓↗𝜑, 𝜒↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into ax-2
3386	→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓𝜑→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3384, 3385
3387	→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3382, 3386
3388	→→¬↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓↔↔𝜑𝜓¬↔𝜑¬𝜓	Subs [𝜑↗↔↔𝜑𝜓¬↔𝜑¬𝜓] into pm2.18
3389	↔↔𝜑𝜓¬↔𝜑¬𝜓	Modus ponens 3387, 3388	pm5.18
3390	↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓	Subs [𝜑↗↔𝜑¬𝜓] into notnotb
3391	→↔↔𝜑𝜓¬↔𝜑¬𝜓↔¬↔𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑¬𝜓] into bicom1
3392	↔¬↔𝜑¬𝜓↔𝜑𝜓	Modus ponens pm5.18, 3391
3393	↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑¬𝜓, 𝜓↗↔𝜑𝜓] into notbi
3394	→↔↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓→↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗↔¬↔𝜑¬𝜓↔𝜑𝜓, 𝜓↗↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓] into biimp
3395	→↔¬↔𝜑¬𝜓↔𝜑𝜓↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3393, 3394
3396	↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3392, 3395
3397	→↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into biimp
3398	→¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3396, 3397
3399	→↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬¬↔𝜑¬𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into biimp
3400	→↔𝜑¬𝜓¬¬↔𝜑¬𝜓	Modus ponens 3390, 3399
3401	→→¬¬↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗→¬¬↔𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into ax-1
3402	→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3398, 3401
3403	→→↔𝜑¬𝜓→¬¬↔𝜑¬𝜓¬↔𝜑𝜓→→↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓, 𝜒↗¬↔𝜑𝜓] into ax-2
3404	→→↔𝜑¬𝜓¬¬↔𝜑¬𝜓→↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3402, 3403
3405	→↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3400, 3404
3406	→↔¬¬↔𝜑¬𝜓¬↔𝜑𝜓↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓	Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into bicom1
3407	↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓	Modus ponens 3396, 3406
3408	→↔¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓¬¬↔𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into biimp
3409	→¬↔𝜑𝜓¬¬↔𝜑¬𝜓	Modus ponens 3407, 3408
3410	→↔↔𝜑¬𝜓¬¬↔𝜑¬𝜓↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬¬↔𝜑¬𝜓] into bicom1
3411	↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓	Modus ponens 3390, 3410
3412	→↔¬¬↔𝜑¬𝜓↔𝜑¬𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓	Subs [𝜑↗¬¬↔𝜑¬𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
3413	→¬¬↔𝜑¬𝜓↔𝜑¬𝜓	Modus ponens 3411, 3412
3414	→→¬¬↔𝜑¬𝜓↔𝜑¬𝜓→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓	Subs [𝜑↗→¬¬↔𝜑¬𝜓↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
3415	→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓	Modus ponens 3413, 3414
3416	→→¬↔𝜑𝜓→¬¬↔𝜑¬𝜓↔𝜑¬𝜓→→¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬↔𝜑¬𝜓, 𝜒↗↔𝜑¬𝜓] into ax-2
3417	→→¬↔𝜑𝜓¬¬↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓	Modus ponens 3415, 3416
3418	→¬↔𝜑𝜓↔𝜑¬𝜓	Modus ponens 3409, 3417
3419	→→↔𝜑¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into impbi
3420	→→¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3405, 3419
3421	↔↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3418, 3420
3422	→↔↔𝜑¬𝜓¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜑¬𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into bicom1
3423	↔¬↔𝜑𝜓↔𝜑¬𝜓	Modus ponens 3421, 3422	xor3
3424	→↔↔𝜑¬𝜓↔𝜓¬𝜑→↔𝜑¬𝜓↔𝜓¬𝜑	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into biimp
3425	→↔¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into biimp
3426	→→↔𝜑¬𝜓↔𝜓¬𝜑→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑	Subs [𝜑↗→↔𝜑¬𝜓↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1
3427	→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑	Modus ponens 2882, 3426
3428	→→¬↔𝜑𝜓→↔𝜑¬𝜓↔𝜓¬𝜑→→¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓, 𝜒↗↔𝜓¬𝜑] into ax-2
3429	→→¬↔𝜑𝜓↔𝜑¬𝜓→¬↔𝜑𝜓↔𝜓¬𝜑	Modus ponens 3427, 3428
3430	→¬↔𝜑𝜓↔𝜓¬𝜑	Modus ponens 3418, 3429
3431	→↔↔𝜑¬𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑↔𝜑¬𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1
3432	↔↔𝜓¬𝜑↔𝜑¬𝜓	Modus ponens con2bi, 3431
3433	→↔↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑↔𝜑¬𝜓	Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓] into biimp
3434	→↔¬↔𝜑𝜓↔𝜑¬𝜓↔↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑¬𝜓] into bicom1
3435	→↔↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗↔𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into biimp
3436	→→↔𝜑¬𝜓¬↔𝜑𝜓→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗→↔𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into ax-1
3437	→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 3405, 3436
3438	→→↔𝜓¬𝜑→↔𝜑¬𝜓¬↔𝜑𝜓→→↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑¬↔𝜑𝜓	Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔𝜑¬𝜓, 𝜒↗¬↔𝜑𝜓] into ax-2
3439	→→↔𝜓¬𝜑↔𝜑¬𝜓→↔𝜓¬𝜑¬↔𝜑𝜓	Modus ponens 3437, 3438
3440	→↔𝜓¬𝜑¬↔𝜑𝜓	Modus ponens 2894, 3439
3441	→→¬↔𝜑𝜓↔𝜓¬𝜑→→↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into impbi
3442	→→↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑	Modus ponens 3430, 3441
3443	↔¬↔𝜑𝜓↔𝜓¬𝜑	Modus ponens 3440, 3442
3444	→↔¬↔𝜑𝜓↔𝜓¬𝜑↔↔𝜓¬𝜑¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into bicom1
3445	↔↔𝜓¬𝜑¬↔𝜑𝜓	Modus ponens 3443, 3444
3446	→↔↔𝜓¬𝜑↔¬𝜑𝜓↔↔¬𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗↔¬𝜑𝜓] into bicom1
3447	→↔↔𝜓¬𝜑¬↔𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓	Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into biimp
3448	→→↔𝜓¬𝜑¬↔𝜑𝜓→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓	Subs [𝜑↗→↔𝜓¬𝜑¬↔𝜑𝜓, 𝜓↗↔¬𝜑𝜓] into ax-1
3449	→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓	Modus ponens 3440, 3448
3450	→→↔¬𝜑𝜓→↔𝜓¬𝜑¬↔𝜑𝜓→→↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓¬↔𝜑𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗↔𝜓¬𝜑, 𝜒↗¬↔𝜑𝜓] into ax-2
3451	→→↔¬𝜑𝜓↔𝜓¬𝜑→↔¬𝜑𝜓¬↔𝜑𝜓	Modus ponens 3449, 3450
3452	→↔¬𝜑𝜓¬↔𝜑𝜓	Modus ponens 2876, 3451
3453	→↔↔𝜓¬𝜑¬↔𝜑𝜓↔¬↔𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗↔𝜓¬𝜑, 𝜓↗¬↔𝜑𝜓] into bicom1
3454	→↔¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔𝜓¬𝜑	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑] into biimp
3455	→→↔𝜓¬𝜑↔¬𝜑𝜓→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓	Subs [𝜑↗→↔𝜓¬𝜑↔¬𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
3456	→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓	Modus ponens 2886, 3455
3457	→→¬↔𝜑𝜓→↔𝜓¬𝜑↔¬𝜑𝜓→→¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔¬𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜓¬𝜑, 𝜒↗↔¬𝜑𝜓] into ax-2
3458	→→¬↔𝜑𝜓↔𝜓¬𝜑→¬↔𝜑𝜓↔¬𝜑𝜓	Modus ponens 3456, 3457
3459	→¬↔𝜑𝜓↔¬𝜑𝜓	Modus ponens 3430, 3458
3460	→→↔¬𝜑𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓¬↔𝜑𝜓	Subs [𝜑↗↔¬𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into impbi
3461	→→¬↔𝜑𝜓↔¬𝜑𝜓↔↔¬𝜑𝜓¬↔𝜑𝜓	Modus ponens 3452, 3460
3462	↔↔¬𝜑𝜓¬↔𝜑𝜓	Modus ponens 3459, 3461	nbbn
3463	→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓] into id
3464	→↔→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into ax-1
3465	→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens ibib, 3464
3466	↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into pm5.74
3467	→↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp
3468	→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Modus ponens 3466, 3467
3469	↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Modus ponens 3463, 3468
3470	↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74
3471	→↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3472	→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3470, 3471
3473	↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3465, 3472
3474	→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3475	→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3473, 3474
3476	→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp
3477	→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Modus ponens 3469, 3476
3478	→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into ax-1
3479	→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3475, 3478
3480	→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into ax-2
3481	→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3479, 3480
3482	→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3477, 3481
3483	→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into bicom1
3484	↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Modus ponens 3473, 3483
3485	→↔→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into biimp
3486	→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓	Modus ponens 3484, 3485
3487	→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓] into bicom1
3488	↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 3469, 3487
3489	→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into biimp
3490	→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 3488, 3489
3491	→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into ax-1
3492	→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 3490, 3491
3493	→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒] into ax-2
3494	→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 3492, 3493
3495	→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 3486, 3494
3496	→→→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into impbi
3497	→→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3482, 3496
3498	↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3495, 3497
3499	↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74
3500	→↔→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓] into bicom1
3501	↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Modus ponens 3499, 3500
3502	→↔↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜑↗↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp
3503	→↔→↔→𝜑𝜒→𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Modus ponens 3501, 3502
3504	→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Modus ponens 3498, 3503
3505	→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into id
3506	→↔→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into ax-1
3507	→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3093, 3506
3508	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑↔𝜑𝜓] into pm5.74
3509	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3510	→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3508, 3509
3511	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3505, 3510
3512	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜑𝜓, 𝜒↗→𝜑𝜓] into pm5.74
3513	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into biimp
3514	→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3512, 3513
3515	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3507, 3514
3516	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into biimp
3517	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3515, 3516
3518	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3519	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3511, 3518
3520	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into ax-1
3521	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3517, 3520
3522	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into ax-2
3523	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3521, 3522
3524	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3519, 3523
3525	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into bicom1
3526	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3515, 3525
3527	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into biimp
3528	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 3526, 3527
3529	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓] into bicom1
3530	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Modus ponens 3511, 3529
3531	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into biimp
3532	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Modus ponens 3530, 3531
3533	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into ax-1
3534	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Modus ponens 3532, 3533
3535	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓, 𝜒↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒] into ax-2
3536	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Modus ponens 3534, 3535
3537	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒	Modus ponens 3528, 3536
3538	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into impbi
3539	→→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3524, 3538
3540	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Modus ponens 3537, 3539
3541	↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜓] into pm5.74
3542	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓] into bicom1
3543	↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3541, 3542
3544	→↔↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓, 𝜓↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓] into biimp
3545	→↔→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜒→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3543, 3544
3546	→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3540, 3545
3547	→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into impbi
3548	→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Modus ponens 3504, 3547
3549	↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Modus ponens 3546, 3548
3550	↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜓↗𝜒, 𝜒↗𝜓] into pm5.74
3551	↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
3552	→↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into bicom1
3553	↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3551, 3552
3554	→↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3555	→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3553, 3554
3556	→↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp
3557	→→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into ax-1
3558	→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3555, 3557
3559	→→↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2
3560	→→↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3558, 3559
3561	→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3504, 3560
3562	→↔↔→𝜑𝜒→𝜑↔𝜑𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3563	→↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into biimp
3564	→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓	Modus ponens 3551, 3563
3565	→↔↔→𝜑𝜒→𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓] into bicom1
3566	↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3549, 3565
3567	→↔↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp
3568	→→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1
3569	→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3546, 3568
3570	→→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑↔𝜑𝜓, 𝜒↗↔→𝜑𝜒→𝜑𝜓] into ax-2
3571	→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑↔𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3569, 3570
3572	→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3564, 3571
3573	→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi
3574	→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3561, 3573
3575	↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3572, 3574
3576	→↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3577	→↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp
3578	→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3550, 3577
3579	→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into ax-1
3580	→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3561, 3579
3581	→→→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2
3582	→→→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3580, 3581
3583	→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3578, 3582
3584	→↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3585	↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Modus ponens 3575, 3584
3586	→↔→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into biimp
3587	→↔→𝜑↔𝜒𝜓↔→𝜑𝜒→𝜑𝜓↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓	Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓] into bicom1
3588	↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓	Modus ponens 3550, 3587
3589	→↔↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓	Subs [𝜑↗↔→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into biimp
3590	→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓	Modus ponens 3588, 3589
3591	→→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓	Subs [𝜑↗→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1
3592	→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓	Modus ponens 3590, 3591
3593	→→→𝜑↔𝜒↔𝜑𝜓→↔→𝜑𝜒→𝜑𝜓→𝜑↔𝜒𝜓→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑↔𝜒𝜓] into ax-2
3594	→→→𝜑↔𝜒↔𝜑𝜓↔→𝜑𝜒→𝜑𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓	Modus ponens 3592, 3593
3595	→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓	Modus ponens 3572, 3594
3596	→→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi
3597	→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3583, 3596
3598	↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3595, 3597
3599	↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜓↗↔𝜒𝜓, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3600	→↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓] into bicom1
3601	↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓	Modus ponens 3599, 3600
3602	→↔↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓] into biimp
3603	→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓	Modus ponens 3601, 3602
3604	→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓	Modus ponens 3598, 3603
3605	↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒] into bicom
3606	→↔↔𝜓𝜒↔𝜒𝜓→𝜑↔↔𝜓𝜒↔𝜒𝜓	Subs [𝜑↗↔↔𝜓𝜒↔𝜒𝜓, 𝜓↗𝜑] into ax-1
3607	→𝜑↔↔𝜓𝜒↔𝜒𝜓	Modus ponens 2677, 3606
3608	↔→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓	Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜒𝜓] into pm5.74
3609	→↔→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓	Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓] into biimp
3610	→→𝜑↔↔𝜓𝜒↔𝜒𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓	Modus ponens 3608, 3609
3611	↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓	Modus ponens 3607, 3610
3612	→↔→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓] into biimp
3613	→→𝜑↔↔𝜒𝜓↔𝜒↔𝜑𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3599, 3612
3614	→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3615	→↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓] into biimp
3616	→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓	Modus ponens 3611, 3615
3617	→→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
3618	→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3583, 3617
3619	→→→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓, 𝜒↗→𝜑↔𝜒↔𝜑𝜓] into ax-2
3620	→→→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3618, 3619
3621	→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3616, 3620
3622	→↔→𝜑↔𝜒𝜓→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓	Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3623	↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓	Modus ponens 3598, 3622
3624	→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓] into biimp
3625	→↔→𝜑↔𝜓𝜒→𝜑↔𝜒𝜓↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒𝜓] into bicom1
3626	↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒	Modus ponens 3611, 3625
3627	→↔→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜒𝜓, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3628	→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒	Modus ponens 3626, 3627
3629	→→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into ax-1
3630	→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒	Modus ponens 3628, 3629
3631	→→→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜒𝜓→𝜑↔𝜓𝜒→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜒𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
3632	→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜒𝜓→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Modus ponens 3630, 3631
3633	→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Modus ponens 3595, 3632
3634	→→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into impbi
3635	→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3621, 3634
3636	↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3633, 3635
3637	↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3638	→↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓] into bicom1
3639	↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓	Modus ponens 3637, 3638
3640	→↔↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓] into biimp
3641	→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓	Modus ponens 3639, 3640
3642	→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓	Modus ponens 3636, 3641
3643	→↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into bicom1
3644	↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Modus ponens 3605, 3643
3645	→↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Subs [𝜑↗↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
3646	→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Modus ponens 3644, 3645
3647	→↔→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓] into biimp
3648	→→𝜑↔↔𝜓𝜒↔𝜒↔𝜑𝜓↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3637, 3647
3649	↔→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Subs [𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3650	→↔→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒] into biimp
3651	→→𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3649, 3650
3652	↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3646, 3651
3653	→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into biimp
3654	→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3652, 3653
3655	→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3656	→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
3657	→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3654, 3656
3658	→→→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓, 𝜒↗→𝜑↔↔𝜑𝜓𝜒] into ax-2
3659	→→→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3657, 3658
3660	→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3621, 3659
3661	→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into bicom1
3662	↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3652, 3661
3663	→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into biimp
3664	→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓	Modus ponens 3662, 3663
3665	→↔→𝜑↔𝜓𝜒→𝜑↔𝜒↔𝜑𝜓↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓] into bicom1
3666	↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Modus ponens 3636, 3665
3667	→↔→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜒↔𝜑𝜓, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3668	→→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Subs [𝜑↗→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into ax-1
3669	→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒	Modus ponens 3633, 3668
3670	→→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜒↔𝜑𝜓→𝜑↔𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜒↔𝜑𝜓, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
3671	→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜒↔𝜑𝜓→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 3669, 3670
3672	→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 3664, 3671
3673	→→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into impbi
3674	→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3660, 3673
3675	↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3672, 3674
3676	↔→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3677	→↔→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒] into bicom1
3678	↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3676, 3677
3679	→↔↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒] into biimp
3680	→↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3678, 3679
3681	→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3675, 3680
3682	→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜓↗↔𝜓𝜒] into pm5.501
3683	↔↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into bicom
3684	→↔↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Subs [𝜑↗↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜓𝜒] into biimp
3685	→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Modus ponens 3683, 3684
3686	→→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Subs [𝜑↗→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒, 𝜓↗𝜑] into ax-1
3687	→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Modus ponens 3685, 3686
3688	→→𝜑→↔↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓𝜒→→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Subs [𝜓↗↔↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜒↗↔↔↔𝜑𝜓𝜒↔𝜓𝜒] into ax-2
3689	→→𝜑↔↔𝜓𝜒↔↔𝜑𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Modus ponens 3687, 3688
3690	→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒	Modus ponens 3681, 3689
3691	↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜓𝜒] into pm5.74
3692	→↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒, 𝜓↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒] into biimp
3693	→→𝜑↔↔↔𝜑𝜓𝜒↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 3691, 3692
3694	↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 3690, 3693
3695	↔→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
3696	→↔→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒] into biimp
3697	→→𝜑↔↔𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3695, 3696
3698	↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3682, 3697
3699	→↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into biimp
3700	→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3698, 3699
3701	→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3702	→→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into ax-1
3703	→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3700, 3702
3704	→→→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→𝜑↔𝜑↔𝜓𝜒] into ax-2
3705	→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3703, 3704
3706	→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3672, 3705
3707	→↔→𝜑↔𝜓𝜒→𝜑↔𝜑↔𝜓𝜒↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into bicom1
3708	↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 3698, 3707
3709	→↔→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
3710	→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 3708, 3709
3711	→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒] into bicom1
3712	→↔→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔𝜑𝜓𝜒] into biimp
3713	→→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into ax-1
3714	→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3660, 3713
3715	→→→𝜑↔𝜑↔𝜓𝜒→→𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔𝜓𝜒, 𝜒↗→𝜑↔↔𝜑𝜓𝜒] into ax-2
3716	→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔𝜓𝜒→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3714, 3715
3717	→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒	Modus ponens 3710, 3716
3718	→→→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔𝜑𝜓𝜒, 𝜓↗→𝜑↔𝜑↔𝜓𝜒] into impbi
3719	→→→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔𝜑𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3706, 3718
3720	↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Modus ponens 3717, 3719
3721	↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒	Subs [𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
3722	→↔→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒] into bicom1
3723	↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 3721, 3722
3724	→↔↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒, 𝜓↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into biimp
3725	→↔→𝜑↔↔𝜑𝜓𝜒→𝜑↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 3723, 3724
3726	→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 3720, 3725
3727	↔↔¬𝜓𝜒¬↔𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into nbbn
3728	→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into id
3729	→↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-1
3730	→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3149, 3729
3731	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑¬𝜓] into pm5.74
3732	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3733	→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3731, 3732
3734	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3728, 3733
3735	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74
3736	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3737	→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3735, 3736
3738	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3730, 3737
3739	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into biimp
3740	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3738, 3739
3741	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3742	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3734, 3741
3743	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into ax-1
3744	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3740, 3743
3745	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into ax-2
3746	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3744, 3745
3747	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3742, 3746
3748	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3749	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3738, 3748
3750	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into biimp
3751	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓	Modus ponens 3749, 3750
3752	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓] into bicom1
3753	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Modus ponens 3734, 3752
3754	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into biimp
3755	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Modus ponens 3753, 3754
3756	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into ax-1
3757	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Modus ponens 3755, 3756
3758	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒] into ax-2
3759	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Modus ponens 3757, 3758
3760	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒	Modus ponens 3751, 3759
3761	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into impbi
3762	→→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3747, 3761
3763	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3760, 3762
3764	↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74
3765	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓] into bicom1
3766	↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Modus ponens 3764, 3765
3767	→↔↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp
3768	→↔→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Modus ponens 3766, 3767
3769	→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Modus ponens 3763, 3768
3770	→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into id
3771	→↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into ax-1
3772	→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3319, 3771
3773	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑↔𝜑𝜓] into pm5.74
3774	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp
3775	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3773, 3774
3776	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3770, 3775
3777	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜑𝜓, 𝜒↗→¬𝜑¬𝜓] into pm5.74
3778	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into biimp
3779	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3777, 3778
3780	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3772, 3779
3781	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into biimp
3782	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3780, 3781
3783	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp
3784	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3776, 3783
3785	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into ax-1
3786	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3782, 3785
3787	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into ax-2
3788	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3786, 3787
3789	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3784, 3788
3790	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into bicom1
3791	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3780, 3790
3792	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into biimp
3793	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3791, 3792
3794	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓] into bicom1
3795	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Modus ponens 3776, 3794
3796	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into biimp
3797	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Modus ponens 3795, 3796
3798	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Subs [𝜑↗→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into ax-1
3799	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Modus ponens 3797, 3798
3800	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓, 𝜒↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒] into ax-2
3801	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Modus ponens 3799, 3800
3802	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒	Modus ponens 3793, 3801
3803	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into impbi
3804	→→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3789, 3803
3805	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Modus ponens 3802, 3804
3806	↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑𝜒, 𝜒↗→¬𝜑¬𝜓] into pm5.74
3807	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓] into bicom1
3808	↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3806, 3807
3809	→↔↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓, 𝜓↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3810	→↔→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑𝜒→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3808, 3809
3811	→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3805, 3810
3812	→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into impbi
3813	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Modus ponens 3769, 3812
3814	↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Modus ponens 3811, 3813
3815	↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗𝜒, 𝜒↗¬𝜓] into pm5.74
3816	↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
3817	→↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into bicom1
3818	↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3816, 3817
3819	→↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3820	→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3818, 3819
3821	→↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp
3822	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-1
3823	→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3820, 3822
3824	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2
3825	→→↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3823, 3824
3826	→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3769, 3825
3827	→↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3828	→↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into biimp
3829	→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓	Modus ponens 3816, 3828
3830	→↔↔→¬𝜑𝜒→¬𝜑¬𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓] into bicom1
3831	↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3814, 3830
3832	→↔↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3833	→→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1
3834	→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3811, 3833
3835	→→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓, 𝜒↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into ax-2
3836	→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑↔𝜑𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3834, 3835
3837	→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3829, 3836
3838	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi
3839	→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3826, 3838
3840	↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3837, 3839
3841	→↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3842	→↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3843	→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3815, 3842
3844	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into ax-1
3845	→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3826, 3844
3846	→→→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2
3847	→→→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3845, 3846
3848	→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3843, 3847
3849	→↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3850	↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Modus ponens 3840, 3849
3851	→↔→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into biimp
3852	→↔→¬𝜑↔𝜒¬𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓] into bicom1
3853	↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓	Modus ponens 3815, 3852
3854	→↔↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp
3855	→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓	Modus ponens 3853, 3854
3856	→→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1
3857	→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓	Modus ponens 3855, 3856
3858	→→→¬𝜑↔𝜒↔𝜑𝜓→↔→¬𝜑𝜒→¬𝜑¬𝜓→¬𝜑↔𝜒¬𝜓→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑𝜒→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜒¬𝜓] into ax-2
3859	→→→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑𝜒→¬𝜑¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓	Modus ponens 3857, 3858
3860	→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓	Modus ponens 3837, 3859
3861	→→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi
3862	→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3848, 3861
3863	↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3860, 3862
3864	↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔𝜒¬𝜓, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3865	→↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3866	↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓	Modus ponens 3864, 3865
3867	→↔↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓] into biimp
3868	→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓	Modus ponens 3866, 3867
3869	→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓	Modus ponens 3863, 3868
3870	↔↔¬𝜓𝜒↔𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗𝜒] into bicom
3871	→↔↔¬𝜓𝜒↔𝜒¬𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓	Subs [𝜑↗↔↔¬𝜓𝜒↔𝜒¬𝜓, 𝜓↗¬𝜑] into ax-1
3872	→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓	Modus ponens 3870, 3871
3873	↔→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔𝜒¬𝜓] into pm5.74
3874	→↔→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓] into biimp
3875	→→¬𝜑↔↔¬𝜓𝜒↔𝜒¬𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓	Modus ponens 3873, 3874
3876	↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓	Modus ponens 3872, 3875
3877	→↔→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3878	→→¬𝜑↔↔𝜒¬𝜓↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3864, 3877
3879	→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3880	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp
3881	→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓	Modus ponens 3876, 3880
3882	→→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into ax-1
3883	→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3848, 3882
3884	→→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓, 𝜒↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-2
3885	→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3883, 3884
3886	→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3881, 3885
3887	→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3888	↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓	Modus ponens 3863, 3887
3889	→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓] into biimp
3890	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒¬𝜓↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒¬𝜓] into bicom1
3891	↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒	Modus ponens 3876, 3890
3892	→↔→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔𝜒¬𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3893	→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒	Modus ponens 3891, 3892
3894	→→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into ax-1
3895	→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒	Modus ponens 3893, 3894
3896	→→→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔𝜒¬𝜓→¬𝜑↔¬𝜓𝜒→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔𝜒¬𝜓, 𝜒↗→¬𝜑↔¬𝜓𝜒] into ax-2
3897	→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔𝜒¬𝜓→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Modus ponens 3895, 3896
3898	→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Modus ponens 3860, 3897
3899	→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into impbi
3900	→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3886, 3899
3901	↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3898, 3900
3902	↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔𝜒↔𝜑𝜓] into pm5.74
3903	→↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3904	↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓	Modus ponens 3902, 3903
3905	→↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓] into biimp
3906	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓	Modus ponens 3904, 3905
3907	→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓	Modus ponens 3901, 3906
3908	→↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Subs [𝜑↗↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗¬𝜑] into ax-1
3909	→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Modus ponens 3644, 3908
3910	→↔→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3911	→→¬𝜑↔↔¬𝜓𝜒↔𝜒↔𝜑𝜓↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3902, 3910
3912	↔→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3913	→↔→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3914	→→¬𝜑↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3912, 3913
3915	↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3909, 3914
3916	→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3917	→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3915, 3916
3918	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3919	→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into ax-1
3920	→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3917, 3919
3921	→→→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2
3922	→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3920, 3921
3923	→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3886, 3922
3924	→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3925	↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3915, 3924
3926	→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into biimp
3927	→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓	Modus ponens 3925, 3926
3928	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓] into bicom1
3929	↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Modus ponens 3901, 3928
3930	→↔→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3931	→→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1
3932	→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒	Modus ponens 3898, 3931
3933	→→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜒↔𝜑𝜓→¬𝜑↔¬𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜒↔𝜑𝜓, 𝜒↗→¬𝜑↔¬𝜓𝜒] into ax-2
3934	→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜒↔𝜑𝜓→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒	Modus ponens 3932, 3933
3935	→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒	Modus ponens 3927, 3934
3936	→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into impbi
3937	→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3923, 3936
3938	↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3935, 3937
3939	↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗↔¬𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3940	→↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3941	↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3939, 3940
3942	→↔↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒] into biimp
3943	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3941, 3942
3944	→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3938, 3943
3945	→↔↔¬𝜓𝜒¬↔𝜓𝜒↔¬↔𝜓𝜒↔¬𝜓𝜒	Subs [𝜑↗↔¬𝜓𝜒, 𝜓↗¬↔𝜓𝜒] into bicom1
3946	↔¬↔𝜓𝜒↔¬𝜓𝜒	Modus ponens 3727, 3945
3947	→↔¬↔𝜓𝜒↔¬𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒	Subs [𝜑↗↔¬↔𝜓𝜒↔¬𝜓𝜒, 𝜓↗¬𝜑] into ax-1
3948	→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒	Modus ponens 3946, 3947
3949	↔→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔¬𝜓𝜒] into pm5.74
3950	→↔→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒] into biimp
3951	→→¬𝜑↔¬↔𝜓𝜒↔¬𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒	Modus ponens 3949, 3950
3952	↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒	Modus ponens 3948, 3951
3953	→↔→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3954	→→¬𝜑↔↔¬𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3939, 3953
3955	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp
3956	→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3957	→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒	Modus ponens 3952, 3956
3958	→→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into ax-1
3959	→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3923, 3958
3960	→→→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2
3961	→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3959, 3960
3962	→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3957, 3961
3963	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3964	↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒	Modus ponens 3938, 3963
3965	→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into biimp
3966	→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔¬𝜓𝜒↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒] into bicom1
3967	↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 3952, 3966
3968	→↔→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp
3969	→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 3967, 3968
3970	→→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1
3971	→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 3969, 3970
3972	→→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔¬𝜓𝜒→¬𝜑¬↔𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬𝜓𝜒, 𝜒↗→¬𝜑¬↔𝜓𝜒] into ax-2
3973	→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 3971, 3972
3974	→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 3935, 3973
3975	→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into impbi
3976	→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3962, 3975
3977	↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3974, 3976
3978	↔→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into pm5.74
3979	→↔→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒] into bicom1
3980	↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3978, 3979
3981	→↔↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒] into biimp
3982	→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3980, 3981
3983	→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒	Modus ponens 3977, 3982
3984	→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜓↗↔𝜓𝜒] into nbn2
3985	↔↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Subs [𝜑↗¬↔𝜓𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into bicom
3986	→↔↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Subs [𝜑↗↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒] into biimp
3987	→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Modus ponens 3985, 3986
3988	→→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Subs [𝜑↗→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
3989	→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Modus ponens 3987, 3988
3990	→→¬𝜑→↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒, 𝜒↗↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒] into ax-2
3991	→→¬𝜑↔¬↔𝜓𝜒↔↔𝜑𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Modus ponens 3989, 3990
3992	→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒	Modus ponens 3983, 3991
3993	↔→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗¬↔𝜓𝜒] into pm5.74
3994	→↔→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒, 𝜓↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒] into biimp
3995	→→¬𝜑↔↔↔𝜑𝜓𝜒¬↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 3993, 3994
3996	↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 3992, 3995
3997	↔→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
3998	→↔→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒] into biimp
3999	→→¬𝜑↔¬↔𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 3997, 3998
4000	↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 3984, 3999
4001	→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into biimp
4002	→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 4000, 4001
4003	→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp
4004	→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-1
4005	→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 4002, 4004
4006	→→→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒, 𝜒↗→¬𝜑↔𝜑↔𝜓𝜒] into ax-2
4007	→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 4005, 4006
4008	→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 3974, 4007
4009	→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into bicom1
4010	↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 4000, 4009
4011	→↔→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into biimp
4012	→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒	Modus ponens 4010, 4011
4013	→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑¬↔𝜓𝜒↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒] into bicom1
4014	→↔→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑¬↔𝜓𝜒, 𝜓↗→¬𝜑↔↔𝜑𝜓𝜒] into biimp
4015	→→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into ax-1
4016	→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 3962, 4015
4017	→→→¬𝜑↔𝜑↔𝜓𝜒→→¬𝜑¬↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Subs [𝜑↗→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔𝜓𝜒, 𝜒↗→¬𝜑↔↔𝜑𝜓𝜒] into ax-2
4018	→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑¬↔𝜓𝜒→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 4016, 4017
4019	→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒	Modus ponens 4012, 4018
4020	→→→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔𝜑𝜓𝜒, 𝜓↗→¬𝜑↔𝜑↔𝜓𝜒] into impbi
4021	→→→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔𝜑𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 4008, 4020
4022	↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Modus ponens 4019, 4021
4023	↔→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗↔↔𝜑𝜓𝜒, 𝜒↗↔𝜑↔𝜓𝜒] into pm5.74
4024	→↔→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒] into bicom1
4025	↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4023, 4024
4026	→↔↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into biimp
4027	→↔→¬𝜑↔↔𝜑𝜓𝜒→¬𝜑↔𝜑↔𝜓𝜒→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4025, 4026
4028	→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4022, 4027
4029	→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into id
4030	→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4031	→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4029, 4030
4032	→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into notnotr
4033	→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4034	→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4035	→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4033, 4034
4036	→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4037	→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4035, 4036
4038	→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4032, 4037
4039	→→¬𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4040	→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4031, 4039
4041	→→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4042	→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4040, 4041
4043	→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4044	→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4042, 4043
4045	→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4046	→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
4047	→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑	Modus ponens 4045, 4046
4048	→→¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑] into ax-2
4049	→→¬𝜑¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑	Modus ponens 4047, 4048
4050	→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4051	→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4038, 4050
4052	→→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4053	→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4051, 4052
4054	→→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑, 𝜒↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4055	→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬𝜑→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4053, 4054
4056	→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4045, 4055
4057	→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-3
4058	→→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬𝜑] into ax-1
4059	→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4057, 4058
4060	→→¬𝜑→→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4061	→→¬𝜑→¬¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4059, 4060
4062	→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4056, 4061
4063	→→¬𝜑→↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬𝜑, 𝜓↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜒↗¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4064	→→¬𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4062, 4063
4065	→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4028, 4064
4066	→→¬𝜑¬¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑	Subs [𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-3
4067	→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑	Modus ponens 4065, 4066
4068	→→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-1
4069	→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 3726, 4068
4070	→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→𝜑↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒, 𝜓↗𝜑, 𝜒↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into ax-2
4071	→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒𝜑→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4069, 4070
4072	→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4067, 4071
4073	→→¬↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Subs [𝜑↗↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒] into pm2.18
4074	↔↔↔𝜑𝜓𝜒↔𝜑↔𝜓𝜒	Modus ponens 4072, 4073	biass
4075	→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜑𝜓] into id
4076	→↔↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔𝜒↔𝜑𝜓] into ax-1
4077	→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑	Modus ponens bicom, 4076
4078	↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
4079	→↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp
4080	→→↔𝜒↔𝜑𝜓↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓	Modus ponens 4078, 4079
4081	↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓	Modus ponens 4075, 4080
4082	↔→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜓𝜑] into pm5.74
4083	→↔→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑] into biimp
4084	→→↔𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4082, 4083
4085	↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4077, 4084
4086	→↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into biimp
4087	→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4085, 4086
4088	→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp
4089	→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓	Modus ponens 4081, 4088
4090	→→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓𝜒] into ax-1
4091	→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4087, 4090
4092	→→→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑→→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into ax-2
4093	→→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4091, 4092
4094	→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4089, 4093
4095	→↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓↔𝜓𝜑↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into bicom1
4096	↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓	Modus ponens 4085, 4095
4097	→↔→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into biimp
4098	→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓	Modus ponens 4096, 4097
4099	→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜑𝜓↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒	Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓] into bicom1
4100	↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒	Modus ponens 4081, 4099
4101	→↔→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜑𝜓𝜒] into biimp
4102	→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒	Modus ponens 4100, 4101
4103	→→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒	Subs [𝜑↗→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into ax-1
4104	→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒	Modus ponens 4102, 4103
4105	→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→→↔𝜒↔𝜑𝜓↔𝜑𝜓→↔𝜒↔𝜑𝜓𝜒→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜑𝜓, 𝜒↗→↔𝜒↔𝜑𝜓𝜒] into ax-2
4106	→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜑𝜓→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒	Modus ponens 4104, 4105
4107	→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒	Modus ponens 4098, 4106
4108	→→→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜑𝜓𝜒, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜓𝜑] into impbi
4109	→→→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓𝜒↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4094, 4108
4110	↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑	Modus ponens 4107, 4109
4111	↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜓𝜑] into pm5.74
4112	→↔→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑] into bicom1
4113	↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Modus ponens 4111, 4112
4114	→↔↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Subs [𝜑↗↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑] into biimp
4115	→↔→↔𝜒↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Modus ponens 4113, 4114
4116	→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Modus ponens 4110, 4115
4117	→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑	Subs [𝜑↗↔𝜒↔𝜓𝜑] into id
4118	→↔↔𝜑𝜓↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜑] into bicom1
4119	→↔↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into ax-1
4120	→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓	Modus ponens 3157, 4119
4121	↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑	Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗𝜒, 𝜒↗↔𝜓𝜑] into pm5.74
4122	→↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑, 𝜓↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp
4123	→→↔𝜒↔𝜓𝜑↔𝜒↔𝜓𝜑↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑	Modus ponens 4121, 4122
4124	↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑	Modus ponens 4117, 4123
4125	↔→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔𝜓𝜑, 𝜒↗↔𝜑𝜓] into pm5.74
4126	→↔→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓] into biimp
4127	→→↔𝜒↔𝜓𝜑↔↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4125, 4126
4128	↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4120, 4127
4129	→↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into biimp
4130	→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4128, 4129
4131	→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp
4132	→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑	Modus ponens 4124, 4131
4133	→→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑𝜒] into ax-1
4134	→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4130, 4133
4135	→→→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓→→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜒↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into ax-2
4136	→→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4134, 4135
4137	→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4132, 4136
4138	→↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑↔𝜑𝜓↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into bicom1
4139	↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑	Modus ponens 4128, 4138
4140	→↔→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into biimp
4141	→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑	Modus ponens 4139, 4140
4142	→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜓𝜑↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒	Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑] into bicom1
4143	↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒	Modus ponens 4124, 4142
4144	→↔→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜓↗→↔𝜒↔𝜓𝜑𝜒] into biimp
4145	→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒	Modus ponens 4143, 4144
4146	→→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒	Subs [𝜑↗→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into ax-1
4147	→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒	Modus ponens 4145, 4146
4148	→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→→↔𝜒↔𝜓𝜑↔𝜓𝜑→↔𝜒↔𝜓𝜑𝜒→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜓𝜑, 𝜒↗→↔𝜒↔𝜓𝜑𝜒] into ax-2
4149	→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒	Modus ponens 4147, 4148
4150	→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒	Modus ponens 4141, 4149
4151	→→→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜓𝜑𝜒, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜑𝜓] into impbi
4152	→→→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑𝜒↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4137, 4151
4153	↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓	Modus ponens 4150, 4152
4154	↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
4155	→↔→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓] into bicom1
4156	↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Modus ponens 4154, 4155
4157	→↔↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓, 𝜓↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓] into biimp
4158	→↔→↔𝜒↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Modus ponens 4156, 4157
4159	→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Modus ponens 4153, 4158
4160	→→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into impbi
4161	→→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Modus ponens 4116, 4160
4162	↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Modus ponens 4159, 4161
4163	↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗↔𝜓𝜑] into bicom
4164	→↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒	Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4165	→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒	Modus ponens 4163, 4164
4166	→↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into biimp
4167	→→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into ax-1
4168	→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒	Modus ponens 4165, 4167
4169	→→↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒→→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑, 𝜒↗↔↔𝜓𝜑𝜒] into ax-2
4170	→→↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Modus ponens 4168, 4169
4171	→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Modus ponens 4116, 4170
4172	→↔↔𝜒↔𝜓𝜑↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑	Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1
4173	↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑	Modus ponens 4163, 4172
4174	→↔↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑	Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜓𝜑] into biimp
4175	→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑	Modus ponens 4173, 4174
4176	→↔↔𝜒↔𝜑𝜓↔𝜒↔𝜓𝜑↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓𝜑] into bicom1
4177	↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Modus ponens 4162, 4176
4178	→↔↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜓𝜑, 𝜓↗↔𝜒↔𝜑𝜓] into biimp
4179	→→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into ax-1
4180	→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓	Modus ponens 4159, 4179
4181	→→↔↔𝜓𝜑𝜒→↔𝜒↔𝜓𝜑↔𝜒↔𝜑𝜓→→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜓𝜑, 𝜒↗↔𝜒↔𝜑𝜓] into ax-2
4182	→→↔↔𝜓𝜑𝜒↔𝜒↔𝜓𝜑→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓	Modus ponens 4180, 4181
4183	→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓	Modus ponens 4175, 4182
4184	→→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into impbi
4185	→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Modus ponens 4171, 4184
4186	↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Modus ponens 4183, 4185
4187	→↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4188	→↔↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into biimp
4189	→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓	Modus ponens 3605, 4188
4190	→→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into ax-1
4191	→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒	Modus ponens 4171, 4190
4192	→→↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒→→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜓𝜑𝜒] into ax-2
4193	→→↔↔𝜑𝜓𝜒↔𝜒↔𝜑𝜓→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒	Modus ponens 4191, 4192
4194	→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒	Modus ponens 4189, 4193
4195	→↔↔𝜒↔𝜑𝜓↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1
4196	↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓	Modus ponens 4186, 4195
4197	→↔↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓	Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓] into biimp
4198	→↔↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Subs [𝜑↗↔𝜒↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓𝜒] into biimp
4199	→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Modus ponens 3644, 4198
4200	→→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Subs [𝜑↗→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into ax-1
4201	→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒	Modus ponens 4199, 4200
4202	→→↔↔𝜓𝜑𝜒→↔𝜒↔𝜑𝜓↔↔𝜑𝜓𝜒→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓𝜒] into ax-2
4203	→→↔↔𝜓𝜑𝜒↔𝜒↔𝜑𝜓→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Modus ponens 4201, 4202
4204	→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Modus ponens 4183, 4203
4205	→→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into impbi
4206	→→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒	Modus ponens 4194, 4205
4207	↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒	Modus ponens 4204, 4206
4208	↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑] into biass
4209	→↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into biimp
4210	→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒	Modus ponens 4208, 4209
4211	→↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4212	→→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into ax-1
4213	→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒	Modus ponens 4210, 4212
4214	→→↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒→→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒, 𝜒↗↔𝜓↔𝜑𝜒] into ax-2
4215	→→↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒	Modus ponens 4213, 4214
4216	→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒	Modus ponens 4194, 4215
4217	→↔↔↔𝜓𝜑𝜒↔𝜓↔𝜑𝜒↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒	Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into bicom1
4218	↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒	Modus ponens 4208, 4217
4219	→↔↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒	Subs [𝜑↗↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into biimp
4220	→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒	Modus ponens 4218, 4219
4221	→↔↔↔𝜑𝜓𝜒↔↔𝜓𝜑𝜒↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔↔𝜓𝜑𝜒] into bicom1
4222	↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Modus ponens 4207, 4221
4223	→↔↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗↔↔𝜓𝜑𝜒, 𝜓↗↔↔𝜑𝜓𝜒] into biimp
4224	→→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into ax-1
4225	→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒	Modus ponens 4204, 4224
4226	→→↔𝜓↔𝜑𝜒→↔↔𝜓𝜑𝜒↔↔𝜑𝜓𝜒→→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒	Subs [𝜑↗↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜓𝜑𝜒, 𝜒↗↔↔𝜑𝜓𝜒] into ax-2
4227	→→↔𝜓↔𝜑𝜒↔↔𝜓𝜑𝜒→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒	Modus ponens 4225, 4226
4228	→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒	Modus ponens 4220, 4227
4229	→→↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒→→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑𝜓𝜒, 𝜓↗↔𝜓↔𝜑𝜒] into impbi
4230	→→↔𝜓↔𝜑𝜒↔↔𝜑𝜓𝜒↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒	Modus ponens 4216, 4229
4231	↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒	Modus ponens 4228, 4230
4232	↔↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜒, 𝜒↗↔𝜓↔𝜑𝜒] into biass
4233	→↔↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒] into biimp
4234	→↔↔↔𝜑𝜓𝜒↔𝜓↔𝜑𝜒↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒	Modus ponens 4232, 4233
4235	↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒	Modus ponens 4231, 4234
4236	↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗𝜒, 𝜒↗↔𝜑𝜒] into biass
4237	→↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into bicom1
4238	↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒	Modus ponens 4236, 4237
4239	→↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into biimp
4240	→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒	Modus ponens 4238, 4239
4241	→↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into biimp
4242	→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒	Modus ponens 4235, 4241
4243	→→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
4244	→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒	Modus ponens 4240, 4243
4245	→→↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒, 𝜒↗↔↔𝜒𝜓↔𝜑𝜒] into ax-2
4246	→→↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒	Modus ponens 4244, 4245
4247	→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒	Modus ponens 4242, 4246
4248	→↔↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒𝜓↔𝜑𝜒↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into bicom1
4249	→↔↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into biimp
4250	→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒	Modus ponens 4236, 4249
4251	→↔↔𝜑𝜓↔𝜒↔𝜓↔𝜑𝜒↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒] into bicom1
4252	↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓	Modus ponens 4235, 4251
4253	→↔↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜒↔𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into biimp
4254	→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓	Modus ponens 4252, 4253
4255	→→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓	Subs [𝜑↗→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into ax-1
4256	→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓	Modus ponens 4254, 4255
4257	→→↔↔𝜒𝜓↔𝜑𝜒→↔𝜒↔𝜓↔𝜑𝜒↔𝜑𝜓→→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓	Subs [𝜑↗↔↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜒↔𝜓↔𝜑𝜒, 𝜒↗↔𝜑𝜓] into ax-2
4258	→→↔↔𝜒𝜓↔𝜑𝜒↔𝜒↔𝜓↔𝜑𝜒→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓	Modus ponens 4256, 4257
4259	→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓	Modus ponens 4250, 4258
4260	→→↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒→→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜒𝜓↔𝜑𝜒] into impbi
4261	→→↔↔𝜒𝜓↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒	Modus ponens 4247, 4260
4262	↔↔𝜑𝜓↔↔𝜒𝜓↔𝜑𝜒	Modus ponens 4259, 4261	biluk
4263	↔↔𝜑𝜑¬↔𝜑¬𝜑	Subs [𝜓↗𝜑] into pm5.18
4264	→↔↔𝜑𝜑¬↔𝜑¬𝜑→↔𝜑𝜑¬↔𝜑¬𝜑	Subs [𝜑↗↔𝜑𝜑, 𝜓↗¬↔𝜑¬𝜑] into biimp
4265	→↔𝜑𝜑¬↔𝜑¬𝜑	Modus ponens 4263, 4264
4266	¬↔𝜑¬𝜑	Modus ponens biid, 4265	pm5.19
4267	→→𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm2.04
4268	→→→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜓→𝜑𝜒] into impbi
4269	→→→𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Modus ponens pm2.04, 4268
4270	↔→𝜑→𝜓𝜒→𝜓→𝜑𝜒	Modus ponens 4267, 4269	bi2.04
4271	↔→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓	Subs [𝜓↗→𝜑𝜓, 𝜒↗𝜓] into pm5.74
4272	→↔→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓→→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑↔→𝜑𝜓𝜓, 𝜓↗↔→𝜑→𝜑𝜓→𝜑𝜓] into biimp
4273	→→𝜑↔→𝜑𝜓𝜓↔→𝜑→𝜑𝜓→𝜑𝜓	Modus ponens 4271, 4272
4274	↔→𝜑→𝜑𝜓→𝜑𝜓	Modus ponens pm5.5, 4273	pm5.4
4275	→→→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into impbi
4276	→→→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens ax-2, 4275
4277	↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens pm2.86, 4276	imdi
4278	→↔→𝜑→𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into bicom1
4279	↔→→𝜑𝜓→𝜑𝜒→𝜑→𝜓𝜒	Modus ponens imdi, 4278	pm5.41
4280	→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into imbi2
4281	→↔→𝜑→𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑→𝜑𝜓	Subs [𝜑↗→𝜑→𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1
4282	↔→𝜑𝜓→𝜑→𝜑𝜓	Modus ponens pm5.4, 4281
4283	→↔→𝜑𝜓→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗↔→𝜑𝜓𝜒] into ax-1
4284	→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓	Modus ponens 4282, 4283
4285	↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜑𝜓] into pm5.74
4286	→↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp
4287	→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Modus ponens 4285, 4286
4288	↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Modus ponens 4284, 4287
4289	↔→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑→𝜑𝜓, 𝜒↗→𝜑𝜒] into pm5.74
4290	→↔→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒] into biimp
4291	→→↔→𝜑𝜓𝜒↔→𝜑→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4289, 4290
4292	↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4280, 4291
4293	→↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into biimp
4294	→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4292, 4293
4295	→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp
4296	→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Modus ponens 4288, 4295
4297	→→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜓] into ax-1
4298	→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4294, 4297
4299	→→→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓𝜒→𝜑𝜒] into ax-2
4300	→→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4298, 4299
4301	→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4296, 4300
4302	→↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into bicom1
4303	↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Modus ponens 4292, 4302
4304	→↔→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into biimp
4305	→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓	Modus ponens 4303, 4304
4306	→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓] into bicom1
4307	↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 4288, 4306
4308	→↔→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜓] into biimp
4309	→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 4307, 4308
4310	→→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into ax-1
4311	→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 4309, 4310
4312	→→→↔→𝜑𝜓𝜒→𝜑𝜒→→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜓→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓𝜒→𝜑𝜓] into ax-2
4313	→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑→𝜑𝜓→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 4311, 4312
4314	→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 4305, 4313
4315	→→→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗→↔→𝜑𝜓𝜒→𝜑𝜒] into impbi
4316	→→→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑𝜓↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4301, 4315
4317	↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Modus ponens 4314, 4316
4318	↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into pm5.74
4319	→↔→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒, 𝜓↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒] into bicom1
4320	↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 4318, 4319
4321	→↔↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒, 𝜓↗→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒] into biimp
4322	→↔→↔→𝜑𝜓𝜒→𝜑𝜓→↔→𝜑𝜓𝜒→𝜑𝜒→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 4320, 4321
4323	→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒	Modus ponens 4317, 4322
4324	→↔→𝜑↔𝜓𝜒↔→𝜑𝜓→𝜑𝜒↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒] into bicom1
4325	↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens pm5.74, 4324
4326	→↔↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
4327	→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒, 𝜓↗↔→𝜑𝜓𝜒] into ax-1
4328	→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 1905, 4327
4329	→→↔→𝜑𝜓𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗↔→𝜑𝜓𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
4330	→→↔→𝜑𝜓𝜒↔→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 4328, 4329
4331	→↔→𝜑𝜓𝜒→𝜑↔𝜓𝜒	Modus ponens 4323, 4330	imbibi
4332	→→→𝜑¬𝜑¬𝜑→→¬𝜑→𝜑¬𝜑↔→𝜑¬𝜑¬𝜑	Subs [𝜑↗→𝜑¬𝜑, 𝜓↗¬𝜑] into impbi
4333	→→¬𝜑→𝜑¬𝜑↔→𝜑¬𝜑¬𝜑	Modus ponens pm2.01, 4332
4334	↔→𝜑¬𝜑¬𝜑	Modus ponens 414, 4333	pm4.8
4335	→→→¬𝜑𝜑𝜑→→𝜑→¬𝜑𝜑↔→¬𝜑𝜑𝜑	Subs [𝜑↗→¬𝜑𝜑, 𝜓↗𝜑] into impbi
4336	→→𝜑→¬𝜑𝜑↔→¬𝜑𝜑𝜑	Modus ponens pm2.18, 4335
4337	↔→¬𝜑𝜑𝜑	Modus ponens 322, 4336	pm4.81
4338	↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜒, 𝜒↗𝜃] into bi2.04
4339	→𝜑↔→𝜑𝜒𝜒	Subs [𝜓↗𝜒] into pm5.5
4340	↔↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒] into bicom
4341	→↔↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜒𝜒, 𝜓↗↔𝜒→𝜑𝜒] into biimp
4342	→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒	Modus ponens 4340, 4341
4343	→→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4344	→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒	Modus ponens 4342, 4343
4345	→→𝜑→↔→𝜑𝜒𝜒↔𝜒→𝜑𝜒→→𝜑↔→𝜑𝜒𝜒→𝜑↔𝜒→𝜑𝜒	Subs [𝜓↗↔→𝜑𝜒𝜒, 𝜒↗↔𝜒→𝜑𝜒] into ax-2
4346	→→𝜑↔→𝜑𝜒𝜒→𝜑↔𝜒→𝜑𝜒	Modus ponens 4344, 4345
4347	→𝜑↔𝜒→𝜑𝜒	Modus ponens 4339, 4346
4348	→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒] into biimp
4349	→→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒	Subs [𝜑↗→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4350	→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒	Modus ponens 4348, 4349
4351	→→𝜑→↔𝜒→𝜑𝜒→𝜒→𝜑𝜒→→𝜑↔𝜒→𝜑𝜒→𝜑→𝜒→𝜑𝜒	Subs [𝜓↗↔𝜒→𝜑𝜒, 𝜒↗→𝜒→𝜑𝜒] into ax-2
4352	→→𝜑↔𝜒→𝜑𝜒→𝜑→𝜒→𝜑𝜒	Modus ponens 4350, 4351
4353	→𝜑→𝜒→𝜑𝜒	Modus ponens 4347, 4352
4354	→→𝜒→𝜑𝜒→𝜒→𝜒→𝜑𝜒	Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗𝜒] into ax-1
4355	→𝜒→𝜒→𝜑𝜒	Modus ponens 1834, 4354
4356	→→𝜒→𝜒→𝜑𝜒→→𝜒𝜒→𝜒→𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
4357	→→𝜒𝜒→𝜒→𝜑𝜒	Modus ponens 4355, 4356
4358	→→𝜑→𝜒→𝜑𝜒→→𝜑𝜒→𝜑→𝜑𝜒	Subs [𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
4359	→→𝜑𝜒→𝜑→𝜑𝜒	Modus ponens 4353, 4358
4360	→→→𝜑𝜒→𝜑→𝜑𝜒→𝜒→→𝜑𝜒→𝜑→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒→𝜑→𝜑𝜒, 𝜓↗𝜒] into ax-1
4361	→𝜒→→𝜑𝜒→𝜑→𝜑𝜒	Modus ponens 4359, 4360
4362	→→𝜒→→𝜑𝜒→𝜑→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→𝜑→𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→𝜑𝜒] into ax-2
4363	→→𝜒→𝜑𝜒→𝜒→𝜑→𝜑𝜒	Modus ponens 4361, 4362
4364	→𝜒→𝜑→𝜑𝜒	Modus ponens 1834, 4363
4365	→→𝜒→𝜑→𝜑𝜒→→𝜒𝜑→𝜒→𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗→𝜑𝜒] into ax-2
4366	→→𝜒𝜑→𝜒→𝜑𝜒	Modus ponens 4364, 4365
4367	→→→𝜒𝜑→𝜒→𝜑𝜒→𝜑→→𝜒𝜑→𝜒→𝜑𝜒	Subs [𝜑↗→→𝜒𝜑→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4368	→𝜑→→𝜒𝜑→𝜒→𝜑𝜒	Modus ponens 4366, 4367
4369	→→𝜑→→𝜒𝜑→𝜒→𝜑𝜒→→𝜑→𝜒𝜑→𝜑→𝜒→𝜑𝜒	Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜒→𝜑𝜒] into ax-2
4370	→→𝜑→𝜒𝜑→𝜑→𝜒→𝜑𝜒	Modus ponens 4368, 4369
4371	→𝜑→𝜃𝜃	Subs [𝜓↗𝜃] into idd
4372	→→𝜃𝜃→→𝜑𝜒→𝜃𝜃	Subs [𝜑↗→𝜃𝜃, 𝜓↗→𝜑𝜒] into ax-1
4373	→→→𝜃𝜃→→𝜑𝜒→𝜃𝜃→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃	Subs [𝜑↗→→𝜃𝜃→→𝜑𝜒→𝜃𝜃, 𝜓↗𝜑] into ax-1
4374	→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃	Modus ponens 4372, 4373
4375	→→𝜑→→𝜃𝜃→→𝜑𝜒→𝜃𝜃→→𝜑→𝜃𝜃→𝜑→→𝜑𝜒→𝜃𝜃	Subs [𝜓↗→𝜃𝜃, 𝜒↗→→𝜑𝜒→𝜃𝜃] into ax-2
4376	→→𝜑→𝜃𝜃→𝜑→→𝜑𝜒→𝜃𝜃	Modus ponens 4374, 4375
4377	→𝜑→→𝜑𝜒→𝜃𝜃	Modus ponens 4371, 4376
4378	→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜃, 𝜒↗𝜃] into ax-2
4379	→→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜑↗→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4380	→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4378, 4379
4381	→→𝜑→→→𝜑𝜒→𝜃𝜃→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜑𝜒→𝜃𝜃→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜓↗→→𝜑𝜒→𝜃𝜃, 𝜒↗→→→𝜑𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4382	→→𝜑→→𝜑𝜒→𝜃𝜃→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4380, 4381
4383	→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4377, 4382
4384	→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒	Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗→→𝜑𝜒𝜃] into ax-1
4385	→→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒	Subs [𝜑↗→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4386	→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒	Modus ponens 4384, 4385
4387	→→𝜑→→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→𝜑→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒	Subs [𝜓↗→𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒𝜃→𝜒→𝜑𝜒] into ax-2
4388	→→𝜑→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒	Modus ponens 4386, 4387
4389	→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒	Modus ponens 4353, 4388
4390	→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜃] into imim2
4391	→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Subs [𝜑↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜓↗→→𝜑𝜒𝜃] into ax-1
4392	→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Modus ponens 4390, 4391
4393	→→→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→→𝜑𝜒𝜃, 𝜒↗→→𝜒→𝜑𝜒→𝜒𝜃] into ax-2
4394	→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Modus ponens 4392, 4393
4395	→→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Subs [𝜑↗→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜓↗𝜑] into ax-1
4396	→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Modus ponens 4394, 4395
4397	→→𝜑→→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Subs [𝜓↗→→→𝜑𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃] into ax-2
4398	→→𝜑→→→𝜑𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Modus ponens 4396, 4397
4399	→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃	Modus ponens 4383, 4398
4400	→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→𝜒→𝜑𝜒, 𝜒↗→𝜒𝜃] into ax-2
4401	→→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4402	→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4400, 4401
4403	→→𝜑→→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜓↗→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4404	→→𝜑→→→𝜑𝜒𝜃→→𝜒→𝜑𝜒→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4402, 4403
4405	→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4399, 4404
4406	→→𝜑→→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒→𝜑𝜒, 𝜒↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4407	→→𝜑→→→𝜑𝜒𝜃→𝜒→𝜑𝜒→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4405, 4406
4408	→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4389, 4407
4409	→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒] into biimp
4410	→→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒	Subs [𝜑↗→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒, 𝜓↗𝜑] into ax-1
4411	→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒	Modus ponens 4409, 4410
4412	→→𝜑→↔→𝜑𝜒𝜒→→𝜑𝜒𝜒→→𝜑↔→𝜑𝜒𝜒→𝜑→→𝜑𝜒𝜒	Subs [𝜓↗↔→𝜑𝜒𝜒, 𝜒↗→→𝜑𝜒𝜒] into ax-2
4413	→→𝜑↔→𝜑𝜒𝜒→𝜑→→𝜑𝜒𝜒	Modus ponens 4411, 4412
4414	→→𝜃𝜃→𝜒→𝜃𝜃	Subs [𝜑↗→𝜃𝜃, 𝜓↗𝜒] into ax-1
4415	→→→𝜃𝜃→𝜒→𝜃𝜃→𝜑→→𝜃𝜃→𝜒→𝜃𝜃	Subs [𝜑↗→→𝜃𝜃→𝜒→𝜃𝜃, 𝜓↗𝜑] into ax-1
4416	→𝜑→→𝜃𝜃→𝜒→𝜃𝜃	Modus ponens 4414, 4415
4417	→→𝜑→→𝜃𝜃→𝜒→𝜃𝜃→→𝜑→𝜃𝜃→𝜑→𝜒→𝜃𝜃	Subs [𝜓↗→𝜃𝜃, 𝜒↗→𝜒→𝜃𝜃] into ax-2
4418	→→𝜑→𝜃𝜃→𝜑→𝜒→𝜃𝜃	Modus ponens 4416, 4417
4419	→𝜑→𝜒→𝜃𝜃	Modus ponens 4371, 4418
4420	→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃	Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗𝜃] into ax-2
4421	→→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4422	→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃	Modus ponens 4420, 4421
4423	→→𝜑→→𝜒→𝜃𝜃→→𝜒𝜃→𝜒𝜃→→𝜑→𝜒→𝜃𝜃→𝜑→→𝜒𝜃→𝜒𝜃	Subs [𝜓↗→𝜒→𝜃𝜃, 𝜒↗→→𝜒𝜃→𝜒𝜃] into ax-2
4424	→→𝜑→𝜒→𝜃𝜃→𝜑→→𝜒𝜃→𝜒𝜃	Modus ponens 4422, 4423
4425	→𝜑→→𝜒𝜃→𝜒𝜃	Modus ponens 4419, 4424
4426	→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒	Subs [𝜑↗→→𝜑𝜒𝜒, 𝜓↗→𝜒𝜃] into ax-1
4427	→→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒	Subs [𝜑↗→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒, 𝜓↗𝜑] into ax-1
4428	→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒	Modus ponens 4426, 4427
4429	→→𝜑→→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜒	Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜒𝜃→→𝜑𝜒𝜒] into ax-2
4430	→→𝜑→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜒	Modus ponens 4428, 4429
4431	→𝜑→→𝜒𝜃→→𝜑𝜒𝜒	Modus ponens 264, 4430
4432	→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Subs [𝜑↗𝜒, 𝜓↗𝜃, 𝜒↗→𝜑𝜒] into imim2
4433	→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Subs [𝜑↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
4434	→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Modus ponens 4432, 4433
4435	→→→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→→→𝜑𝜒𝜒→→𝜑𝜒𝜃] into ax-2
4436	→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Modus ponens 4434, 4435
4437	→→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Subs [𝜑↗→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4438	→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Modus ponens 4436, 4437
4439	→→𝜑→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Subs [𝜓↗→→𝜒𝜃→𝜒𝜃, 𝜒↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃] into ax-2
4440	→→𝜑→→𝜒𝜃→𝜒𝜃→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Modus ponens 4438, 4439
4441	→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃	Modus ponens 4425, 4440
4442	→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→𝜑𝜒𝜃] into ax-2
4443	→→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜑↗→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4444	→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4442, 4443
4445	→→𝜑→→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜓↗→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃, 𝜒↗→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4446	→→𝜑→→𝜒𝜃→→→𝜑𝜒𝜒→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4444, 4445
4447	→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4441, 4446
4448	→→𝜑→→→𝜒𝜃→→𝜑𝜒𝜒→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜓↗→→𝜒𝜃→→𝜑𝜒𝜒, 𝜒↗→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4449	→→𝜑→→𝜒𝜃→→𝜑𝜒𝜒→𝜑→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4447, 4448
4450	→𝜑→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4431, 4449
4451	→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into impbi
4452	→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜑↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4453	→→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜑↗→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃, 𝜓↗𝜑] into ax-1
4454	→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4452, 4453
4455	→→𝜑→→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→𝜑→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃	Subs [𝜓↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃] into ax-2
4456	→→𝜑→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4454, 4455
4457	→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃	Modus ponens 4450, 4456
4458	→→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜒𝜃→→𝜑𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4459	→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4451, 4458
4460	→→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4461	→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4459, 4460
4462	→→𝜑→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜓↗→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃, 𝜒↗→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4463	→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜒𝜃→→𝜑𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4461, 4462
4464	→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4457, 4463
4465	→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃] into id
4466	→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4467	→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4468	→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4466, 4467
4469	→→→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑→→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4470	→→→→→𝜑𝜒𝜃→𝜒𝜃→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4468, 4469
4471	→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4472	→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4464, 4471
4473	→→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4474	→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4472, 4473
4475	→→→→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗→𝜑→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4476	→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4474, 4475
4477	→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4466, 4476
4478	→→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4479	→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4477, 4478
4480	→→𝜑→→→→𝜑𝜒𝜃→𝜒𝜃→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜓↗→→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4481	→→𝜑→→→𝜑𝜒𝜃→𝜒𝜃→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4479, 4480
4482	→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4408, 4481
4483	→→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜓↗𝜑, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4484	→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4482, 4483
4485	→→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗𝜑] into ax-1
4486	→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4484, 4485
4487	→→𝜑→→𝜑𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜑→𝜑𝜑→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4488	→→𝜑→𝜑𝜑→𝜑→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4486, 4487
4489	→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens id, 4484
4490	→→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-1
4491	→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4489, 4490
4492	→→𝜓→𝜑↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃	Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗↔→→𝜑𝜒𝜃→𝜒𝜃] into ax-2
4493	→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃	Modus ponens 4491, 4492
4494	↔→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜒𝜃, 𝜒↗→𝜒𝜃] into pm5.74
4495	→↔→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Subs [𝜑↗→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜓↗↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃] into biimp
4496	→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Modus ponens 4494, 4495
4497	→→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Subs [𝜑↗→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃, 𝜓↗→𝜓𝜑] into ax-1
4498	→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Modus ponens 4496, 4497
4499	→→→𝜓𝜑→→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃, 𝜒↗↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃] into ax-2
4500	→→→𝜓𝜑→𝜓↔→→𝜑𝜒𝜃→𝜒𝜃→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Modus ponens 4498, 4499
4501	→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃	Modus ponens 4493, 4500
4502	→↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃	Subs [𝜑↗↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃, 𝜓↗→𝜓𝜑] into ax-1
4503	→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃	Modus ponens 4338, 4502
4504	↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜒→𝜓𝜃, 𝜒↗→𝜓→→𝜑𝜒𝜃] into pm5.74
4505	→↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Subs [𝜑↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃, 𝜓↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp
4506	→→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Modus ponens 4504, 4505
4507	↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Modus ponens 4503, 4506
4508	↔→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓→→𝜑𝜒𝜃, 𝜒↗→𝜓→𝜒𝜃] into pm5.74
4509	→↔→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Subs [𝜑↗→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃, 𝜓↗↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃] into biimp
4510	→→→𝜓𝜑↔→𝜓→→𝜑𝜒𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4508, 4509
4511	↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4501, 4510
4512	→↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into biimp
4513	→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4511, 4512
4514	→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp
4515	→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Modus ponens 4507, 4514
4516	→→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Subs [𝜑↗→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into ax-1
4517	→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4513, 4516
4518	→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜒↗→→𝜓𝜑→𝜓→𝜒𝜃] into ax-2
4519	→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4517, 4518
4520	→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4515, 4519
4521	→↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→𝜓→𝜒𝜃↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into bicom1
4522	↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Modus ponens 4511, 4521
4523	→↔→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into biimp
4524	→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃	Modus ponens 4522, 4523
4525	→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃] into bicom1
4526	↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Modus ponens 4507, 4525
4527	→↔→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜓↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into biimp
4528	→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Modus ponens 4526, 4527
4529	→→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Subs [𝜑↗→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into ax-1
4530	→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Modus ponens 4528, 4529
4531	→→→→𝜓𝜑→𝜓→𝜒𝜃→→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑→𝜓→→𝜑𝜒𝜃, 𝜒↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃] into ax-2
4532	→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→𝜓→→𝜑𝜒𝜃→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Modus ponens 4530, 4531
4533	→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃	Modus ponens 4524, 4532
4534	→→→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜒→𝜓𝜃, 𝜓↗→→𝜓𝜑→𝜓→𝜒𝜃] into impbi
4535	→→→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑→→𝜑𝜒→𝜓𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4520, 4534
4536	↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Modus ponens 4533, 4535
4537	↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃	Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜒→𝜓𝜃, 𝜒↗→𝜓→𝜒𝜃] into pm5.74
4538	→↔→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃	Subs [𝜑↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃, 𝜓↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃] into bicom1
4539	↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃	Modus ponens 4537, 4538
4540	→↔↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃	Subs [𝜑↗↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃, 𝜓↗→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃] into biimp
4541	→↔→→𝜓𝜑→→𝜑𝜒→𝜓𝜃→→𝜓𝜑→𝜓→𝜒𝜃→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃	Modus ponens 4539, 4540
4542	→→𝜓𝜑↔→→𝜑𝜒→𝜓𝜃→𝜓→𝜒𝜃	Modus ponens 4536, 4541	imim21b
4543	→↔⋀𝜑𝜓¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into bicom1
4544	↔¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens df-an, 4543	pm4.63
4545	↔¬→¬𝜑¬𝜓⋀¬𝜑𝜓	Subs [𝜑↗¬𝜑] into pm4.63	pm4.67
4546	↔→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓] into notnotb
4547	↔↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓] into notbi
4548	→↔↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓→↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓] into biimp
4549	→↔¬→𝜑¬𝜓⋀𝜑𝜓↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens 4547, 4548
4550	↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens pm4.63, 4549
4551	→↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into biimp
4552	→¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens 4550, 4551
4553	→↔→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into biimp
4554	→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 4546, 4553
4555	→→¬¬→𝜑¬𝜓¬⋀𝜑𝜓→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗→¬¬→𝜑¬𝜓¬⋀𝜑𝜓, 𝜓↗→𝜑¬𝜓] into ax-1
4556	→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens 4552, 4555
4557	→→→𝜑¬𝜓→¬¬→𝜑¬𝜓¬⋀𝜑𝜓→→→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓, 𝜒↗¬⋀𝜑𝜓] into ax-2
4558	→→→𝜑¬𝜓¬¬→𝜑¬𝜓→→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens 4556, 4557
4559	→→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens 4554, 4558
4560	→↔¬¬→𝜑¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into bicom1
4561	↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓	Modus ponens 4550, 4560
4562	→↔¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬¬→𝜑¬𝜓] into biimp
4563	→¬⋀𝜑𝜓¬¬→𝜑¬𝜓	Modus ponens 4561, 4562
4564	→↔→𝜑¬𝜓¬¬→𝜑¬𝜓↔¬¬→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬¬→𝜑¬𝜓] into bicom1
4565	↔¬¬→𝜑¬𝜓→𝜑¬𝜓	Modus ponens 4546, 4564
4566	→↔¬¬→𝜑¬𝜓→𝜑¬𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗¬¬→𝜑¬𝜓, 𝜓↗→𝜑¬𝜓] into biimp
4567	→→¬¬→𝜑¬𝜓→𝜑¬𝜓→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓	Subs [𝜑↗→¬¬→𝜑¬𝜓→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into ax-1
4568	→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓	Modus ponens 501, 4567
4569	→→¬⋀𝜑𝜓→¬¬→𝜑¬𝜓→𝜑¬𝜓→→¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓→𝜑¬𝜓	Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬¬→𝜑¬𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
4570	→→¬⋀𝜑𝜓¬¬→𝜑¬𝜓→¬⋀𝜑𝜓→𝜑¬𝜓	Modus ponens 4568, 4569
4571	→¬⋀𝜑𝜓→𝜑¬𝜓	Modus ponens 4563, 4570
4572	→→→𝜑¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓→𝜑¬𝜓↔→𝜑¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗¬⋀𝜑𝜓] into impbi
4573	→→¬⋀𝜑𝜓→𝜑¬𝜓↔→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens 4559, 4572
4574	↔→𝜑¬𝜓¬⋀𝜑𝜓	Modus ponens 4571, 4573	imnan
4575	→↔𝜓¬¬𝜓→𝜑↔𝜓¬¬𝜓	Subs [𝜑↗↔𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
4576	→𝜑↔𝜓¬¬𝜓	Modus ponens 1915, 4575
4577	↔→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓	Subs [𝜒↗¬¬𝜓] into pm5.74
4578	→↔→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓→→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓	Subs [𝜑↗→𝜑↔𝜓¬¬𝜓, 𝜓↗↔→𝜑𝜓→𝜑¬¬𝜓] into biimp
4579	→→𝜑↔𝜓¬¬𝜓↔→𝜑𝜓→𝜑¬¬𝜓	Modus ponens 4577, 4578
4580	↔→𝜑𝜓→𝜑¬¬𝜓	Modus ponens 4576, 4579
4581	↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓	Subs [𝜓↗¬𝜓] into imnan
4582	→↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓	Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗¬⋀𝜑¬𝜓] into biimp
4583	→→𝜑¬¬𝜓¬⋀𝜑¬𝜓	Modus ponens 4581, 4582
4584	→↔→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into biimp
4585	→→𝜑𝜓→𝜑¬¬𝜓	Modus ponens 4580, 4584
4586	→→→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓	Subs [𝜑↗→→𝜑¬¬𝜓¬⋀𝜑¬𝜓, 𝜓↗→𝜑𝜓] into ax-1
4587	→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓	Modus ponens 4583, 4586
4588	→→→𝜑𝜓→→𝜑¬¬𝜓¬⋀𝜑¬𝜓→→→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓¬⋀𝜑¬𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗¬⋀𝜑¬𝜓] into ax-2
4589	→→→𝜑𝜓→𝜑¬¬𝜓→→𝜑𝜓¬⋀𝜑¬𝜓	Modus ponens 4587, 4588
4590	→→𝜑𝜓¬⋀𝜑¬𝜓	Modus ponens 4585, 4589
4591	→↔→𝜑¬¬𝜓¬⋀𝜑¬𝜓↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓	Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗¬⋀𝜑¬𝜓] into bicom1
4592	↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓	Modus ponens 4581, 4591
4593	→↔¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑¬¬𝜓	Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑¬¬𝜓] into biimp
4594	→¬⋀𝜑¬𝜓→𝜑¬¬𝜓	Modus ponens 4592, 4593
4595	→↔→𝜑𝜓→𝜑¬¬𝜓↔→𝜑¬¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into bicom1
4596	↔→𝜑¬¬𝜓→𝜑𝜓	Modus ponens 4580, 4595
4597	→↔→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗→𝜑𝜓] into biimp
4598	→→𝜑¬¬𝜓→𝜑𝜓	Modus ponens 4596, 4597
4599	→→→𝜑¬¬𝜓→𝜑𝜓→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑¬¬𝜓→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into ax-1
4600	→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓	Modus ponens 4598, 4599
4601	→→¬⋀𝜑¬𝜓→→𝜑¬¬𝜓→𝜑𝜓→→¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗→𝜑𝜓] into ax-2
4602	→→¬⋀𝜑¬𝜓→𝜑¬¬𝜓→¬⋀𝜑¬𝜓→𝜑𝜓	Modus ponens 4600, 4601
4603	→¬⋀𝜑¬𝜓→𝜑𝜓	Modus ponens 4594, 4602
4604	→→→𝜑𝜓¬⋀𝜑¬𝜓→→¬⋀𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓¬⋀𝜑¬𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into impbi
4605	→→¬⋀𝜑¬𝜓→𝜑𝜓↔→𝜑𝜓¬⋀𝜑¬𝜓	Modus ponens 4590, 4604
4606	↔→𝜑𝜓¬⋀𝜑¬𝜓	Modus ponens 4603, 4605	iman
4607	↔→𝜑𝜑¬⋀𝜑¬𝜑	Subs [𝜓↗𝜑] into iman
4608	→↔→𝜑𝜑¬⋀𝜑¬𝜑→→𝜑𝜑¬⋀𝜑¬𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗¬⋀𝜑¬𝜑] into biimp
4609	→→𝜑𝜑¬⋀𝜑¬𝜑	Modus ponens 4607, 4608
4610	¬⋀𝜑¬𝜑	Modus ponens id, 4609	pm3.24
4611	↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓	Subs [𝜑↗⋀𝜑¬𝜓] into notnotb
4612	→↔→𝜑𝜓¬⋀𝜑¬𝜓↔¬⋀𝜑¬𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬⋀𝜑¬𝜓] into bicom1
4613	↔¬⋀𝜑¬𝜓→𝜑𝜓	Modus ponens iman, 4612
4614	↔↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Subs [𝜑↗¬⋀𝜑¬𝜓, 𝜓↗→𝜑𝜓] into notbi
4615	→↔↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓→↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Subs [𝜑↗↔¬⋀𝜑¬𝜓→𝜑𝜓, 𝜓↗↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓] into biimp
4616	→↔¬⋀𝜑¬𝜓→𝜑𝜓↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4614, 4615
4617	↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4613, 4616
4618	→↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into biimp
4619	→¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4617, 4618
4620	→↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓	Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into biimp
4621	→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓	Modus ponens 4611, 4620
4622	→→¬¬⋀𝜑¬𝜓¬→𝜑𝜓→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Subs [𝜑↗→¬¬⋀𝜑¬𝜓¬→𝜑𝜓, 𝜓↗⋀𝜑¬𝜓] into ax-1
4623	→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4619, 4622
4624	→→⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓¬→𝜑𝜓→→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬→𝜑𝜓	Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
4625	→→⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓→⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4623, 4624
4626	→⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4621, 4625
4627	→↔¬¬⋀𝜑¬𝜓¬→𝜑𝜓↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓	Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into bicom1
4628	↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓	Modus ponens 4617, 4627
4629	→↔¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓¬¬⋀𝜑¬𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into biimp
4630	→¬→𝜑𝜓¬¬⋀𝜑¬𝜓	Modus ponens 4628, 4629
4631	→↔⋀𝜑¬𝜓¬¬⋀𝜑¬𝜓↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓	Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬¬⋀𝜑¬𝜓] into bicom1
4632	↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓	Modus ponens 4611, 4631
4633	→↔¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓	Subs [𝜑↗¬¬⋀𝜑¬𝜓, 𝜓↗⋀𝜑¬𝜓] into biimp
4634	→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓	Modus ponens 4632, 4633
4635	→→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓	Subs [𝜑↗→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
4636	→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓	Modus ponens 4634, 4635
4637	→→¬→𝜑𝜓→¬¬⋀𝜑¬𝜓⋀𝜑¬𝜓→→¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓⋀𝜑¬𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬⋀𝜑¬𝜓, 𝜒↗⋀𝜑¬𝜓] into ax-2
4638	→→¬→𝜑𝜓¬¬⋀𝜑¬𝜓→¬→𝜑𝜓⋀𝜑¬𝜓	Modus ponens 4636, 4637
4639	→¬→𝜑𝜓⋀𝜑¬𝜓	Modus ponens 4630, 4638
4640	→→⋀𝜑¬𝜓¬→𝜑𝜓→→¬→𝜑𝜓⋀𝜑¬𝜓↔⋀𝜑¬𝜓¬→𝜑𝜓	Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into impbi
4641	→→¬→𝜑𝜓⋀𝜑¬𝜓↔⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4626, 4640
4642	↔⋀𝜑¬𝜓¬→𝜑𝜓	Modus ponens 4639, 4641	annim
4643	→↔⋀𝜑¬𝜓¬→𝜑𝜓↔¬→𝜑𝜓⋀𝜑¬𝜓	Subs [𝜑↗⋀𝜑¬𝜓, 𝜓↗¬→𝜑𝜓] into bicom1
4644	↔¬→𝜑𝜓⋀𝜑¬𝜓	Modus ponens annim, 4643	pm4.61
4645	↔¬→¬𝜑𝜓⋀¬𝜑¬𝜓	Subs [𝜑↗¬𝜑] into pm4.61	pm4.65
4646	→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒] into id
4647	→⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓] into id
4648	→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4649	→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓	Subs [𝜑↗→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
4650	→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓	Modus ponens 4648, 4649
4651	→→⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒⋀𝜑𝜓] into ax-2
4652	→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓	Modus ponens 4650, 4651
4653	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-2
4654	→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4646, 4653
4655	→→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
4656	→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4654, 4655
4657	→→⋀𝜑𝜓→→→⋀𝜑𝜓𝜒⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→⋀𝜑𝜓𝜒⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2
4658	→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4656, 4657
4659	→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4648, 4658
4660	→↔¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓] into biimp
4661	→¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens pm4.63, 4660
4662	→→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
4663	→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4659, 4662
4664	→→¬→𝜑¬𝜓→⋀𝜑𝜓→→⋀𝜑𝜓𝜒𝜒→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2
4665	→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4663, 4664
4666	→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4661, 4665
4667	→→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-1
4668	→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4666, 4667
4669	→→𝜓→¬→𝜑¬𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→→⋀𝜑𝜓𝜒𝜒] into ax-2
4670	→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4668, 4669
4671	→→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4672	→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4670, 4671
4673	→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-2
4674	→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4672, 4673
4675	→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens pm3.2im, 4674
4676	→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗𝜒] into pm2.27
4677	→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒	Subs [𝜑↗→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜓↗𝜑] into ax-1
4678	→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒	Modus ponens 4676, 4677
4679	→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4680	→→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜑↗→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4681	→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4679, 4680
4682	→→𝜑→→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒	Subs [𝜓↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒] into ax-2
4683	→→𝜑→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4681, 4682
4684	→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒	Modus ponens 4675, 4683
4685	→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓𝜒𝜒, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
4686	→→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Subs [𝜑↗→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4687	→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Modus ponens 4685, 4686
4688	→→→⋀𝜑𝜓𝜒→→→→⋀𝜑𝜓𝜒𝜒𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜒↗→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒] into ax-2
4689	→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Modus ponens 4687, 4688
4690	→→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
4691	→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Modus ponens 4689, 4690
4692	→→𝜑→→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Subs [𝜓↗→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒] into ax-2
4693	→→𝜑→→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Modus ponens 4691, 4692
4694	→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒	Modus ponens 4678, 4693
4695	→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→𝜓𝜒] into ax-2
4696	→→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
4697	→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 4695, 4696
4698	→→𝜑→→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜓↗→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒, 𝜒↗→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
4699	→→𝜑→→⋀𝜑𝜓𝜒→→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 4697, 4698
4700	→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 4694, 4699
4701	→→𝜑→→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
4702	→→𝜑→→⋀𝜑𝜓𝜒→𝜓→→⋀𝜑𝜓𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 4700, 4701
4703	→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 4684, 4702
4704	→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
4705	→→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4706	→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒	Modus ponens 4704, 4705
4707	→→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→⋀𝜑𝜓𝜒] into ax-2
4708	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒	Modus ponens 4706, 4707
4709	→→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
4710	→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 4703, 4709
4711	→→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
4712	→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 4710, 4711
4713	→→→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
4714	→→→⋀𝜑𝜓𝜒→𝜑→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 4712, 4713
4715	→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Modus ponens 4704, 4714	pm3.3
4716	→𝜓→→𝜑→𝜓𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1
4717	→→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→𝜓→→𝜑→𝜓𝜒𝜓	Subs [𝜑↗→𝜓→→𝜑→𝜓𝜒𝜓] into ax-1
4718	→𝜓→𝜓→→𝜑→𝜓𝜒𝜓	Modus ponens 4716, 4717
4719	→→𝜓→𝜓→→𝜑→𝜓𝜒𝜓→→𝜓𝜓→𝜓→→𝜑→𝜓𝜒𝜓	Subs [𝜑↗𝜓, 𝜒↗→→𝜑→𝜓𝜒𝜓] into ax-2
4720	→→𝜓𝜓→𝜓→→𝜑→𝜓𝜒𝜓	Modus ponens 4718, 4719
4721	→→→𝜑→𝜓𝜒→𝜓→𝜑𝜒→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
4722	→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens pm2.04, 4721
4723	→→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1
4724	→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 4722, 4723
4725	→→𝜓→→→𝜑→𝜓𝜒𝜓→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜓, 𝜒↗→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
4726	→→𝜓→→𝜑→𝜓𝜒𝜓→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 4724, 4725
4727	→𝜓→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 4716, 4726
4728	→→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→𝜑𝜒𝜒	Subs [𝜑↗→𝜑→→𝜑𝜒𝜒] into ax-1
4729	→𝜓→𝜑→→𝜑𝜒𝜒	Modus ponens 264, 4728
4730	→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜓↗𝜑] into ax-1
4731	→→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒] into ax-1
4732	→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 4730, 4731
4733	→→𝜓→→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→𝜑→→𝜑→𝜓𝜒→𝜑𝜒] into ax-2
4734	→→𝜓→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 4732, 4733
4735	→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒	Modus ponens 4727, 4734
4736	→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜒, 𝜒↗→𝜑→𝜓𝜒] into imim2
4737	→→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4738	→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Modus ponens 4736, 4737
4739	→→𝜑→→→𝜑𝜒𝜒→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Subs [𝜓↗→→𝜑𝜒𝜒, 𝜒↗→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-2
4740	→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Modus ponens 4738, 4739
4741	→→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-1
4742	→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Modus ponens 4740, 4741
4743	→→𝜓→→𝜑→→𝜑𝜒𝜒→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑𝜒𝜒, 𝜒↗→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒] into ax-2
4744	→→𝜓→𝜑→→𝜑𝜒𝜒→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Modus ponens 4742, 4743
4745	→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒	Modus ponens 4729, 4744
4746	→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒	Subs [𝜓↗→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4747	→→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒] into ax-1
4748	→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4746, 4747
4749	→→𝜓→→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒, 𝜒↗→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2
4750	→→𝜓→𝜑→→→𝜑→𝜓𝜒→𝜑𝜒→→𝜑→𝜓𝜒𝜒→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4748, 4749
4751	→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4745, 4750
4752	→→𝜓→→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑→𝜓𝜒→𝜑𝜒, 𝜒↗→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2
4753	→→𝜓→𝜑→→𝜑→𝜓𝜒→𝜑𝜒→𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4751, 4752
4754	→𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4735, 4753
4755	→→𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4756	→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4754, 4755
4757	→→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4758	→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4756, 4757
4759	→→𝜑→→𝜓𝜑→𝜓→→𝜑→𝜓𝜒𝜒→→𝜑→𝜓𝜑→𝜑→𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓→→𝜑→𝜓𝜒𝜒] into ax-2
4760	→→𝜑→𝜓𝜑→𝜑→𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4758, 4759
4761	→𝜑→𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens ax-1, 4760
4762	→→𝜑→𝜓→→𝜑→𝜓𝜒𝜒→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Subs [𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4763	→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4761, 4762
4764	→→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1
4765	→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4763, 4764
4766	→→¬¬𝜓→→𝜑𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→→𝜑→𝜓𝜒𝜒] into ax-2
4767	→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 4765, 4766
4768	→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒	Modus ponens 575, 4767
4769	→→¬¬𝜓→𝜑→→𝜑→𝜓𝜒𝜒→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4770	→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4768, 4769
4771	→→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4772	→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4770, 4771
4773	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓→→𝜑→𝜓𝜒𝜒] into ax-2
4774	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4772, 4773
4775	→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 581, 4774
4776	→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒𝜒] into notnot
4777	→→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1
4778	→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4776, 4777
4779	→→¬¬𝜓→→→𝜑→𝜓𝜒𝜒¬¬→→𝜑→𝜓𝜒𝜒→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→→𝜑→𝜓𝜒𝜒, 𝜒↗¬¬→→𝜑→𝜓𝜒𝜒] into ax-2
4780	→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4778, 4779
4781	→→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4782	→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4780, 4781
4783	→→𝜑→→¬¬𝜓→→𝜑→𝜓𝜒𝜒→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒	Subs [𝜓↗→¬¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒] into ax-2
4784	→→𝜑→¬¬𝜓→→𝜑→𝜓𝜒𝜒→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4782, 4783
4785	→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4775, 4784
4786	→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-3
4787	→→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓, 𝜓↗𝜑] into ax-1
4788	→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓	Modus ponens 4786, 4787
4789	→→𝜑→→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒¬𝜓→→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓	Subs [𝜓↗→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬𝜓] into ax-2
4790	→→𝜑→¬¬𝜓¬¬→→𝜑→𝜓𝜒𝜒→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓	Modus ponens 4788, 4789
4791	→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓	Modus ponens 4785, 4790
4792	→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒] into id
4793	→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
4794	→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4795	→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4793, 4794
4796	→→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→𝜑¬→→𝜑→𝜓𝜒𝜒] into ax-2
4797	→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4795, 4796
4798	→→𝜑→¬→→𝜑→𝜓𝜒𝜒¬𝜓→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓	Subs [𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗¬𝜓] into ax-2
4799	→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓	Modus ponens 4791, 4798
4800	→→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4801	→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓	Modus ponens 4799, 4800
4802	→→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→𝜑¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→𝜑¬𝜓] into ax-2
4803	→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓	Modus ponens 4801, 4802
4804	→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓	Modus ponens 4793, 4803
4805	→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4806	→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 619, 4805
4807	→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4808	→→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4809	→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Modus ponens 4807, 4808
4810	→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓] into ax-2
4811	→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Modus ponens 4809, 4810
4812	→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Modus ponens 622, 4811
4813	→→¬→→𝜑→𝜓𝜒𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
4814	→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Modus ponens 4806, 4813
4815	→→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Subs [𝜑↗→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4816	→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Modus ponens 4814, 4815
4817	→→¬¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓, 𝜒↗→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓] into ax-2
4818	→→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓	Modus ponens 4816, 4817
4819	→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4820	→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4821	→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4819, 4820
4822	→→¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒] into ax-2
4823	→→¬→→𝜑→𝜓𝜒𝜒¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒	Modus ponens 4821, 4822
4824	→→¬¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒, 𝜒↗¬→𝜑¬𝜓] into ax-2
4825	→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4812, 4824
4826	→→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4827	→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4825, 4826
4828	→→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
4829	→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→→𝜑→𝜓𝜒𝜒→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4827, 4828
4830	→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4819, 4829
4831	→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬→→𝜑→𝜓𝜒𝜒] into ax-1
4832	→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 647, 4831
4833	→→¬→→𝜑→𝜓𝜒𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
4834	→→¬→→𝜑→𝜓𝜒𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 4832, 4833
4835	→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 4830, 4834
4836	→→¬→→𝜑→𝜓𝜒𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓	Subs [𝜑↗¬→→𝜑→𝜓𝜒𝜒, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
4837	→→¬→→𝜑→𝜓𝜒𝜒→𝜑¬𝜓→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓	Modus ponens 4835, 4836
4838	→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓	Modus ponens 4804, 4837
4839	→→¬→→𝜑→𝜓𝜒𝜒¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-3
4840	→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4838, 4839
4841	→↔⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into biimp
4842	→⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens df-an, 4841
4843	→→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
4844	→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4840, 4843
4845	→→⋀𝜑𝜓→¬→𝜑¬𝜓→→𝜑→𝜓𝜒𝜒→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→→𝜑→𝜓𝜒𝜒] into ax-2
4846	→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4844, 4845
4847	→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒	Modus ponens 4842, 4846
4848	→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
4849	→→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
4850	→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒	Modus ponens 4848, 4849
4851	→→→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓→𝜑→𝜓𝜒] into ax-2
4852	→→→𝜑→𝜓𝜒→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒	Modus ponens 4850, 4851
4853	→→⋀𝜑𝜓→→𝜑→𝜓𝜒𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-2
4854	→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 4847, 4853
4855	→→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
4856	→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 4854, 4855
4857	→→→𝜑→𝜓𝜒→→⋀𝜑𝜓→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
4858	→→→𝜑→𝜓𝜒→⋀𝜑𝜓→𝜑→𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 4856, 4857
4859	→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 4848, 4858	pm3.31
4860	→→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into impbi
4861	→→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Modus ponens pm3.3, 4860
4862	↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Modus ponens pm3.31, 4861	impexp
4863	→⋀𝜓𝜑⋀𝜓𝜑	Subs [𝜑↗⋀𝜓𝜑] into id
4864	↔⋀𝜓𝜑¬→𝜓¬𝜑	Subs [𝜑↗𝜓, 𝜓↗𝜑] into df-an
4865	→↔⋀𝜓𝜑¬→𝜓¬𝜑↔¬→𝜓¬𝜑⋀𝜓𝜑	Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into bicom1
4866	↔¬→𝜓¬𝜑⋀𝜓𝜑	Modus ponens 4864, 4865
4867	→↔¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑	Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑] into biimp
4868	→¬→𝜓¬𝜑⋀𝜓𝜑	Modus ponens 4866, 4867
4869	→→⋀𝜓𝜑⋀𝜓𝜑→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑	Subs [𝜑↗→⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into ax-1
4870	→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑	Modus ponens 4863, 4869
4871	→→¬→𝜓¬𝜑→⋀𝜓𝜑⋀𝜓𝜑→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑	Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4872	→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑⋀𝜓𝜑	Modus ponens 4870, 4871
4873	→𝜓→𝜑¬→𝜓¬𝜑	Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm3.2im
4874	→→¬→𝜓¬𝜑⋀𝜓𝜑→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑	Subs [𝜑↗→¬→𝜓¬𝜑⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4875	→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑	Modus ponens 4868, 4874
4876	→→𝜑→¬→𝜓¬𝜑⋀𝜓𝜑→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑	Subs [𝜓↗¬→𝜓¬𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4877	→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑	Modus ponens 4875, 4876
4878	→→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑	Subs [𝜑↗→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑] into ax-1
4879	→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑	Modus ponens 4877, 4878
4880	→→𝜓→→𝜑¬→𝜓¬𝜑→𝜑⋀𝜓𝜑→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑⋀𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗→𝜑¬→𝜓¬𝜑, 𝜒↗→𝜑⋀𝜓𝜑] into ax-2
4881	→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑⋀𝜓𝜑	Modus ponens 4879, 4880
4882	→𝜓→𝜑⋀𝜓𝜑	Modus ponens 4873, 4881
4883	→→𝜓→𝜑⋀𝜓𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4884	→→𝜓𝜑→𝜓⋀𝜓𝜑	Modus ponens 4882, 4883
4885	→→→𝜓𝜑→𝜓⋀𝜓𝜑→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4886	→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑	Modus ponens 4884, 4885
4887	→→𝜑→→𝜓𝜑→𝜓⋀𝜓𝜑→→𝜑→𝜓𝜑→𝜑→𝜓⋀𝜓𝜑	Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓⋀𝜓𝜑] into ax-2
4888	→→𝜑→𝜓𝜑→𝜑→𝜓⋀𝜓𝜑	Modus ponens 4886, 4887
4889	→𝜑→𝜓⋀𝜓𝜑	Modus ponens ax-1, 4888	pm3.21
4890	→→𝜑→𝜓⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜓𝜑	Subs [𝜒↗⋀𝜓𝜑] into ax-2
4891	→→𝜑𝜓→𝜑⋀𝜓𝜑	Modus ponens pm3.21, 4890	ancr
4892	→→→𝜑𝜓→𝜑⋀𝜓𝜑→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑	Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜑, 𝜓↗¬¬𝜓] into ax-1
4893	→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑	Modus ponens ancr, 4892
4894	→→¬¬𝜓→→𝜑𝜓→𝜑⋀𝜓𝜑→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑⋀𝜓𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜓𝜑] into ax-2
4895	→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑⋀𝜓𝜑	Modus ponens 4893, 4894
4896	→¬¬𝜓→𝜑⋀𝜓𝜑	Modus ponens 575, 4895
4897	→→¬¬𝜓→𝜑⋀𝜓𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into ax-2
4898	→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑	Modus ponens 4896, 4897
4899	→→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4900	→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑	Modus ponens 4898, 4899
4901	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓⋀𝜓𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓⋀𝜓𝜑	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓⋀𝜓𝜑] into ax-2
4902	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓⋀𝜓𝜑	Modus ponens 4900, 4901
4903	→𝜑→¬¬𝜓⋀𝜓𝜑	Modus ponens 581, 4902
4904	→⋀𝜓𝜑¬¬⋀𝜓𝜑	Subs [𝜑↗⋀𝜓𝜑] into notnot
4905	→→⋀𝜓𝜑¬¬⋀𝜓𝜑→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑	Subs [𝜑↗→⋀𝜓𝜑¬¬⋀𝜓𝜑, 𝜓↗¬¬𝜓] into ax-1
4906	→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑	Modus ponens 4904, 4905
4907	→→¬¬𝜓→⋀𝜓𝜑¬¬⋀𝜓𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜓𝜑, 𝜒↗¬¬⋀𝜓𝜑] into ax-2
4908	→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑	Modus ponens 4906, 4907
4909	→→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑	Subs [𝜑↗→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4910	→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑	Modus ponens 4908, 4909
4911	→→𝜑→→¬¬𝜓⋀𝜓𝜑→¬¬𝜓¬¬⋀𝜓𝜑→→𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜓𝜑	Subs [𝜓↗→¬¬𝜓⋀𝜓𝜑, 𝜒↗→¬¬𝜓¬¬⋀𝜓𝜑] into ax-2
4912	→→𝜑→¬¬𝜓⋀𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜓𝜑	Modus ponens 4910, 4911
4913	→𝜑→¬¬𝜓¬¬⋀𝜓𝜑	Modus ponens 4903, 4912
4914	→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-3
4915	→→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓, 𝜓↗𝜑] into ax-1
4916	→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓	Modus ponens 4914, 4915
4917	→→𝜑→→¬¬𝜓¬¬⋀𝜓𝜑→¬⋀𝜓𝜑¬𝜓→→𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→¬⋀𝜓𝜑¬𝜓	Subs [𝜓↗→¬¬𝜓¬¬⋀𝜓𝜑, 𝜒↗→¬⋀𝜓𝜑¬𝜓] into ax-2
4918	→→𝜑→¬¬𝜓¬¬⋀𝜓𝜑→𝜑→¬⋀𝜓𝜑¬𝜓	Modus ponens 4916, 4917
4919	→𝜑→¬⋀𝜓𝜑¬𝜓	Modus ponens 4913, 4918
4920	→¬⋀𝜓𝜑¬⋀𝜓𝜑	Subs [𝜑↗¬⋀𝜓𝜑] into id
4921	→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
4922	→→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑	Subs [𝜑↗→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑] into ax-1
4923	→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑	Modus ponens 4921, 4922
4924	→→¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑, 𝜒↗→𝜑¬⋀𝜓𝜑] into ax-2
4925	→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑	Modus ponens 4923, 4924
4926	→→𝜑→¬⋀𝜓𝜑¬𝜓→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓	Subs [𝜓↗¬⋀𝜓𝜑, 𝜒↗¬𝜓] into ax-2
4927	→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓	Modus ponens 4919, 4926
4928	→→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4929	→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓	Modus ponens 4927, 4928
4930	→→¬⋀𝜓𝜑→→𝜑¬⋀𝜓𝜑→𝜑¬𝜓→→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬𝜓	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→𝜑¬⋀𝜓𝜑, 𝜒↗→𝜑¬𝜓] into ax-2
4931	→→¬⋀𝜓𝜑→𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→𝜑¬𝜓	Modus ponens 4929, 4930
4932	→¬⋀𝜓𝜑→𝜑¬𝜓	Modus ponens 4921, 4931
4933	→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4934	→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 619, 4933
4935	→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4936	→→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4937	→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Modus ponens 4935, 4936
4938	→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬⋀𝜓𝜑¬→𝜑¬𝜓] into ax-2
4939	→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Modus ponens 4937, 4938
4940	→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Modus ponens 622, 4939
4941	→→¬⋀𝜓𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
4942	→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Modus ponens 4934, 4941
4943	→→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Subs [𝜑↗→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4944	→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Modus ponens 4942, 4943
4945	→→¬¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬⋀𝜓𝜑¬→𝜑¬𝜓, 𝜒↗→¬⋀𝜓𝜑¬→𝜑¬𝜓] into ax-2
4946	→→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓	Modus ponens 4944, 4945
4947	→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
4948	→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑	Subs [𝜑↗→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑] into ax-1
4949	→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑	Modus ponens 4947, 4948
4950	→→¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗¬⋀𝜓𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑] into ax-2
4951	→→¬⋀𝜓𝜑¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑	Modus ponens 4949, 4950
4952	→→¬¬¬→𝜑¬𝜓→¬⋀𝜓𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2
4953	→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4940, 4952
4954	→→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4955	→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4953, 4954
4956	→→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
4957	→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬⋀𝜓𝜑→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4955, 4956
4958	→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 4947, 4957
4959	→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬⋀𝜓𝜑] into ax-1
4960	→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 647, 4959
4961	→→¬⋀𝜓𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
4962	→→¬⋀𝜓𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 4960, 4961
4963	→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 4958, 4962
4964	→→¬⋀𝜓𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑¬¬→𝜑¬𝜓	Subs [𝜑↗¬⋀𝜓𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
4965	→→¬⋀𝜓𝜑→𝜑¬𝜓→¬⋀𝜓𝜑¬¬→𝜑¬𝜓	Modus ponens 4963, 4964
4966	→¬⋀𝜓𝜑¬¬→𝜑¬𝜓	Modus ponens 4932, 4965
4967	→→¬⋀𝜓𝜑¬¬→𝜑¬𝜓→¬→𝜑¬𝜓⋀𝜓𝜑	Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜑¬𝜓] into ax-3
4968	→¬→𝜑¬𝜓⋀𝜓𝜑	Modus ponens 4966, 4967
4969	→→¬→𝜑¬𝜓⋀𝜓𝜑→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑	Subs [𝜑↗→¬→𝜑¬𝜓⋀𝜓𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
4970	→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑	Modus ponens 4968, 4969
4971	→→⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜓𝜑→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜓𝜑] into ax-2
4972	→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 4970, 4971
4973	→⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 4842, 4972	pm3.22
4974	→⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm3.22
4975	→→⋀𝜑𝜓⋀𝜓𝜑→→⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into impbi
4976	→→⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑	Modus ponens pm3.22, 4975
4977	↔⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 4974, 4976	ancom
4978	→↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀𝜑𝜓𝜒→⋀𝜓𝜑𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into imbi1
4979	↔→⋀𝜑𝜓𝜒→⋀𝜓𝜑𝜒	Modus ponens ancom, 4978	ancomst
4980	→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒] into id
4981	↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜓↗⋀𝜓𝜒] into df-an
4982	→↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into bicom1
4983	↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4981, 4982
4984	→↔¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
4985	→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4983, 4984
4986	→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1
4987	→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4980, 4986
4988	→→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
4989	→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4987, 4988
4990	→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜓↗⋀𝜓𝜒] into pm3.2im
4991	→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
4992	→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4985, 4991
4993	→→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
4994	→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4992, 4993
4995	→→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
4996	→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4994, 4995
4997	→→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒] into ax-2
4998	→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4996, 4997
4999	→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4990, 4998
5000	→⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒] into id
5001	→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5002	→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5003	→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 5001, 5002
5004	→→⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5005	→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 5003, 5004
5006	→→𝜑→⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5007	→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 4999, 5006
5008	→→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5009	→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5007, 5008
5010	→→⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5011	→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5009, 5010
5012	→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5001, 5011
5013	↔⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into df-an
5014	→↔⋀𝜓𝜒¬→𝜓¬𝜒↔¬→𝜓¬𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into bicom1
5015	↔¬→𝜓¬𝜒⋀𝜓𝜒	Modus ponens 5013, 5014
5016	→↔¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒⋀𝜓𝜒	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒] into biimp
5017	→¬→𝜓¬𝜒⋀𝜓𝜒	Modus ponens 5015, 5016
5018	→→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-1
5019	→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5012, 5018
5020	→→¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀𝜑⋀𝜓𝜒→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5021	→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5019, 5020
5022	→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5017, 5021
5023	→𝜓→𝜒¬→𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm3.2im
5024	→→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
5025	→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5022, 5024
5026	→→𝜒→¬→𝜓¬𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5027	→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5025, 5026
5028	→→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-1
5029	→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5027, 5028
5030	→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5031	→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5029, 5030
5032	→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5023, 5031
5033	→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜓↗⋀𝜑⋀𝜓𝜒] into pm2.27
5034	→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5035	→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5033, 5034
5036	→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5037	→→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-1
5038	→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5036, 5037
5039	→→𝜓→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒] into ax-2
5040	→→𝜓→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5038, 5039
5041	→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 5032, 5040
5042	→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into imim2
5043	→→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5044	→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5042, 5043
5045	→→𝜑→→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜓↗→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5046	→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5044, 5045
5047	→→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5048	→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5046, 5047
5049	→→𝜓→→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5050	→→𝜓→𝜑→→𝜑⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5048, 5049
5051	→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5035, 5050
5052	→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜓↗→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5053	→→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5054	→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5052, 5053
5055	→→𝜓→→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5056	→→𝜓→𝜑→→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜒⋀𝜑⋀𝜓𝜒→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5054, 5055
5057	→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5051, 5056
5058	→→𝜓→→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5059	→→𝜓→𝜑→𝜒→𝜑⋀𝜑⋀𝜓𝜒→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5057, 5058
5060	→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5041, 5059
5061	→→𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5062	→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5060, 5061
5063	→→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5064	→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5062, 5063
5065	→→𝜑→→𝜓𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→𝜓𝜑→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5066	→→𝜑→𝜓𝜑→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5064, 5065
5067	→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens ax-1, 5066
5068	→→𝜑→𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5069	→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5067, 5068
5070	→→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
5071	→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5069, 5070
5072	→→¬¬𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5073	→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5071, 5072
5074	→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 575, 5073
5075	→→¬¬𝜓→𝜑→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5076	→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5074, 5075
5077	→→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5078	→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5076, 5077
5079	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5080	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5078, 5079
5081	→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 581, 5080
5082	→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜒⋀𝜑⋀𝜓𝜒] into notnot
5083	→→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
5084	→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5082, 5083
5085	→→¬¬𝜓→→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5086	→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5084, 5085
5087	→→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5088	→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5086, 5087
5089	→→𝜑→→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜓↗→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5090	→→𝜑→¬¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5088, 5089
5091	→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5081, 5090
5092	→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-3
5093	→→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓, 𝜓↗𝜑] into ax-1
5094	→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓	Modus ponens 5092, 5093
5095	→→𝜑→→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓	Subs [𝜓↗→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓] into ax-2
5096	→→𝜑→¬¬𝜓¬¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓	Modus ponens 5094, 5095
5097	→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓	Modus ponens 5091, 5096
5098	→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒] into id
5099	→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5100	→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5101	→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5099, 5100
5102	→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5103	→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5101, 5102
5104	→→𝜑→¬→𝜒⋀𝜑⋀𝜓𝜒¬𝜓→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓	Subs [𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬𝜓] into ax-2
5105	→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓	Modus ponens 5097, 5104
5106	→→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5107	→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓	Modus ponens 5105, 5106
5108	→→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑¬𝜓] into ax-2
5109	→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓	Modus ponens 5107, 5108
5110	→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓	Modus ponens 5099, 5109
5111	→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5112	→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 619, 5111
5113	→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5114	→→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5115	→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Modus ponens 5113, 5114
5116	→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓] into ax-2
5117	→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Modus ponens 5115, 5116
5118	→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Modus ponens 622, 5117
5119	→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
5120	→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Modus ponens 5112, 5119
5121	→→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Subs [𝜑↗→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5122	→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Modus ponens 5120, 5121
5123	→→¬¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓, 𝜒↗→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓] into ax-2
5124	→→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓	Modus ponens 5122, 5123
5125	→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5126	→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5127	→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5125, 5126
5128	→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5129	→→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5127, 5128
5130	→→¬¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗¬→𝜑¬𝜓] into ax-2
5131	→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5118, 5130
5132	→→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5133	→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5131, 5132
5134	→→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
5135	→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜒⋀𝜑⋀𝜓𝜒→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5133, 5134
5136	→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5125, 5135
5137	→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬→𝜒⋀𝜑⋀𝜓𝜒] into ax-1
5138	→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 647, 5137
5139	→→¬→𝜒⋀𝜑⋀𝜓𝜒→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
5140	→→¬→𝜒⋀𝜑⋀𝜓𝜒→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 5138, 5139
5141	→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 5136, 5140
5142	→→¬→𝜒⋀𝜑⋀𝜓𝜒→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
5143	→→¬→𝜒⋀𝜑⋀𝜓𝜒→𝜑¬𝜓→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓	Modus ponens 5141, 5142
5144	→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓	Modus ponens 5110, 5143
5145	→→¬→𝜒⋀𝜑⋀𝜓𝜒¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-3
5146	→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5144, 5145
5147	→→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5148	→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5146, 5147
5149	→→⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5150	→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5148, 5149
5151	→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 4842, 5150
5152	↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into df-an
5153	→¬¬𝜒𝜒	Subs [𝜑↗𝜒] into notnotr
5154	→𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5155	→→𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜒→⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5156	→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒	Modus ponens 5154, 5155
5157	→→¬¬𝜒→𝜒→⋀𝜑𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
5158	→→¬¬𝜒𝜒→¬¬𝜒→⋀𝜑𝜓𝜒	Modus ponens 5156, 5157
5159	→¬¬𝜒→⋀𝜑𝜓𝜒	Modus ponens 5153, 5158
5160	→→⋀𝜑𝜓→𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5161	→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 5151, 5160
5162	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5163	→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 5161, 5162
5164	→→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒] into ax-2
5165	→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 5163, 5164
5166	→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 5159, 5165
5167	→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
5168	→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓	Subs [𝜑↗→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
5169	→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓	Modus ponens 5167, 5168
5170	→→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→¬¬𝜒⋀𝜑𝜓] into ax-2
5171	→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓	Modus ponens 5169, 5170
5172	→→¬¬𝜒→⋀𝜑𝜓⋀𝜑⋀𝜓𝜒→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5173	→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5166, 5172
5174	→→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5175	→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5173, 5174
5176	→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒⋀𝜑⋀𝜓𝜒] into ax-2
5177	→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5175, 5176
5178	→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5167, 5177
5179	→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒] into notnot
5180	→→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5181	→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒	Modus ponens 5179, 5180
5182	→→¬¬𝜒→⋀𝜑⋀𝜓𝜒¬¬⋀𝜑⋀𝜓𝜒→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗¬¬⋀𝜑⋀𝜓𝜒] into ax-2
5183	→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒	Modus ponens 5181, 5182
5184	→→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5185	→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒	Modus ponens 5183, 5184
5186	→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑⋀𝜓𝜒→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒] into ax-2
5187	→→⋀𝜑𝜓→¬¬𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒	Modus ponens 5185, 5186
5188	→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒	Modus ponens 5178, 5187
5189	→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-3
5190	→→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5191	→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒	Modus ponens 5189, 5190
5192	→→⋀𝜑𝜓→→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬𝜒] into ax-2
5193	→→⋀𝜑𝜓→¬¬𝜒¬¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒	Modus ponens 5191, 5192
5194	→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒	Modus ponens 5188, 5193
5195	→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒] into id
5196	→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5197	→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5198	→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒	Modus ponens 5196, 5197
5199	→→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒] into ax-2
5200	→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒	Modus ponens 5198, 5199
5201	→→⋀𝜑𝜓→¬⋀𝜑⋀𝜓𝜒¬𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2
5202	→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 5194, 5201
5203	→→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5204	→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 5202, 5203
5205	→→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
5206	→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 5204, 5205
5207	→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 5196, 5206
5208	→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒] into id
5209	→→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5210	→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5208, 5209
5211	→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒] into notnotr
5212	→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5213	→→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
5214	→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5212, 5213
5215	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
5216	→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5214, 5215
5217	→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5211, 5216
5218	→→¬⋀𝜑⋀𝜓𝜒→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
5219	→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5210, 5218
5220	→→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
5221	→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5219, 5220
5222	→→¬¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
5223	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5221, 5222
5224	→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
5225	→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5226	→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒	Modus ponens 5224, 5225
5227	→→¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒] into ax-2
5228	→→¬⋀𝜑⋀𝜓𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒	Modus ponens 5226, 5227
5229	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
5230	→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5217, 5229
5231	→→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5232	→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5230, 5231
5233	→→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
5234	→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬⋀𝜑⋀𝜓𝜒→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5232, 5233
5235	→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5224, 5234
5236	→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-3
5237	→→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬⋀𝜑⋀𝜓𝜒] into ax-1
5238	→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 5236, 5237
5239	→→¬⋀𝜑⋀𝜓𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2
5240	→→¬⋀𝜑⋀𝜓𝜒→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 5238, 5239
5241	→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 5235, 5240
5242	→→¬⋀𝜑⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬⋀𝜑⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2
5243	→→¬⋀𝜑⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 5241, 5242
5244	→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 5207, 5243
5245	→→¬⋀𝜑⋀𝜓𝜒¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3
5246	→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5244, 5245
5247	→↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into biimp
5248	→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5152, 5247
5249	→→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
5250	→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5246, 5249
5251	→→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
5252	→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5250, 5251
5253	→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5248, 5252
5254	→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒] into id
5255	→↔⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into bicom1
5256	↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5152, 5255
5257	→↔¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
5258	→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5256, 5257
5259	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-1
5260	→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5254, 5259
5261	→→¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5262	→→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5260, 5261
5263	→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into pm3.2im
5264	→→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5265	→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5258, 5264
5266	→→𝜒→¬→⋀𝜑𝜓¬𝜒⋀⋀𝜑𝜓𝜒→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5267	→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5265, 5266
5268	→→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5269	→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5267, 5268
5270	→→⋀𝜑𝜓→→𝜒¬→⋀𝜑𝜓¬𝜒→𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5271	→→⋀𝜑𝜓→𝜒¬→⋀𝜑𝜓¬𝜒→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5269, 5270
5272	→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5263, 5271
5273	→→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬𝜓] into ax-1
5274	→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5272, 5273
5275	→→¬→𝜑¬𝜓→⋀𝜑𝜓→𝜒⋀⋀𝜑𝜓𝜒→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5276	→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5274, 5275
5277	→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 4661, 5276
5278	→→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-1
5279	→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5277, 5278
5280	→→𝜓→¬→𝜑¬𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5281	→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5279, 5280
5282	→→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5283	→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5281, 5282
5284	→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5285	→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5283, 5284
5286	→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens pm3.2im, 5285
5287	→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into pm2.27
5288	→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5289	→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5287, 5288
5290	→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5291	→→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5292	→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5290, 5291
5293	→→𝜑→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5294	→→𝜑→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5292, 5293
5295	→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5286, 5294
5296	→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into imim2
5297	→→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5298	→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5296, 5297
5299	→→𝜒→→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5300	→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5298, 5299
5301	→→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5302	→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5300, 5301
5303	→→𝜑→→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5304	→→𝜑→𝜒→→𝜒⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5302, 5303
5305	→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5289, 5304
5306	→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5307	→→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5308	→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5306, 5307
5309	→→𝜑→→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5310	→→𝜑→𝜒→→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜓⋀⋀𝜑𝜓𝜒→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5308, 5309
5311	→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5305, 5310
5312	→→𝜑→→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜒→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5313	→→𝜑→𝜒→𝜓→𝜒⋀⋀𝜑𝜓𝜒→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5311, 5312
5314	→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5295, 5313
5315	→→𝜑→𝜒→𝜓⋀⋀𝜑𝜓𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜓↗𝜒, 𝜒↗→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5316	→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5314, 5315
5317	→→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5318	→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5316, 5317
5319	→→𝜒→→𝜑𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜑𝜒→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5320	→→𝜒→𝜑𝜒→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5318, 5319
5321	→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 1834, 5320
5322	→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into pm2.27
5323	→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5324	→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5322, 5323
5325	→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-1
5326	→→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5327	→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5325, 5326
5328	→→𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒] into ax-2
5329	→→𝜒→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5327, 5328
5330	→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 5321, 5329
5331	→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into imim2
5332	→→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5333	→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5331, 5332
5334	→→𝜓→→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5335	→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5333, 5334
5336	→→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5337	→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5335, 5336
5338	→→𝜒→→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5339	→→𝜒→𝜓→→𝜓⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5337, 5338
5340	→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5324, 5339
5341	→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5342	→→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
5343	→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5341, 5342
5344	→→𝜒→→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5345	→→𝜒→𝜓→→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5343, 5344
5346	→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5340, 5345
5347	→→𝜒→→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5348	→→𝜒→𝜓→𝜑→𝜓⋀⋀𝜑𝜓𝜒→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5346, 5347
5349	→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5330, 5348
5350	→𝜓→𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜒] into ax-1
5351	→→𝜓→𝜒𝜓→𝜓→𝜓→𝜒𝜓	Subs [𝜑↗→𝜓→𝜒𝜓] into ax-1
5352	→𝜓→𝜓→𝜒𝜓	Modus ponens 5350, 5351
5353	→→𝜓→𝜓→𝜒𝜓→→𝜓𝜓→𝜓→𝜒𝜓	Subs [𝜑↗𝜓, 𝜒↗→𝜒𝜓] into ax-2
5354	→→𝜓𝜓→𝜓→𝜒𝜓	Modus ponens 5352, 5353
5355	→→𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5356	→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5349, 5355
5357	→→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5358	→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5356, 5357
5359	→→𝜓→→𝜒𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→𝜒𝜓→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5360	→→𝜓→𝜒𝜓→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5358, 5359
5361	→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5350, 5360
5362	→𝜒→𝜓𝜒	Subs [𝜑↗𝜒] into ax-1
5363	→→𝜒→𝜓𝜒→¬¬𝜒→𝜒→𝜓𝜒	Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5364	→¬¬𝜒→𝜒→𝜓𝜒	Modus ponens 5362, 5363
5365	→→¬¬𝜒→𝜒→𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2
5366	→→¬¬𝜒𝜒→¬¬𝜒→𝜓𝜒	Modus ponens 5364, 5365
5367	→¬¬𝜒→𝜓𝜒	Modus ponens 5153, 5366
5368	→→𝜓→𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5369	→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5361, 5368
5370	→→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5371	→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5369, 5370
5372	→→¬¬𝜒→→𝜓𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5373	→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5371, 5372
5374	→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5367, 5373
5375	→𝜓→¬¬𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗¬¬𝜒] into ax-1
5376	→→𝜓→¬¬𝜒𝜓→𝜓→𝜓→¬¬𝜒𝜓	Subs [𝜑↗→𝜓→¬¬𝜒𝜓] into ax-1
5377	→𝜓→𝜓→¬¬𝜒𝜓	Modus ponens 5375, 5376
5378	→→𝜓→𝜓→¬¬𝜒𝜓→→𝜓𝜓→𝜓→¬¬𝜒𝜓	Subs [𝜑↗𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2
5379	→→𝜓𝜓→𝜓→¬¬𝜒𝜓	Modus ponens 5377, 5378
5380	→→¬¬𝜒→𝜓→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5381	→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5374, 5380
5382	→→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5383	→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5381, 5382
5384	→→𝜓→→¬¬𝜒𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5385	→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5383, 5384
5386	→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5375, 5385
5387	→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜑⋀⋀𝜑𝜓𝜒] into notnot
5388	→→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
5389	→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5387, 5388
5390	→→¬¬𝜒→→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5391	→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5389, 5390
5392	→→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5393	→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5391, 5392
5394	→→𝜓→→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5395	→→𝜓→¬¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5393, 5394
5396	→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5386, 5395
5397	→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-3
5398	→→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒] into ax-1
5399	→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒	Modus ponens 5397, 5398
5400	→→𝜓→→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒] into ax-2
5401	→→𝜓→¬¬𝜒¬¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒	Modus ponens 5399, 5400
5402	→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒	Modus ponens 5396, 5401
5403	→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒] into id
5404	→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5405	→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5406	→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5404, 5405
5407	→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5408	→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5406, 5407
5409	→→𝜓→¬→𝜑⋀⋀𝜑𝜓𝜒¬𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬𝜒] into ax-2
5410	→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒	Modus ponens 5402, 5409
5411	→→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒	Subs [𝜑↗→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5412	→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒	Modus ponens 5410, 5411
5413	→→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
5414	→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒	Modus ponens 5412, 5413
5415	→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒	Modus ponens 5404, 5414
5416	→¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜓¬𝜒] into id
5417	→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5418	→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5416, 5417
5419	→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜓¬𝜒] into notnotr
5420	→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5421	→→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
5422	→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5420, 5421
5423	→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒] into ax-2
5424	→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5422, 5423
5425	→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5419, 5424
5426	→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
5427	→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5418, 5426
5428	→→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
5429	→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5427, 5428
5430	→→¬¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒, 𝜒↗→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒] into ax-2
5431	→→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5429, 5430
5432	→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
5433	→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5434	→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5432, 5433
5435	→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5436	→→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5434, 5435
5437	→→¬¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
5438	→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5425, 5437
5439	→→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5440	→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5438, 5439
5441	→→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
5442	→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜑⋀⋀𝜑𝜓𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5440, 5441
5443	→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5432, 5442
5444	→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬¬→𝜓¬𝜒, 𝜓↗→𝜓¬𝜒] into ax-3
5445	→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬→𝜑⋀⋀𝜑𝜓𝜒] into ax-1
5446	→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 5444, 5445
5447	→→¬→𝜑⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
5448	→→¬→𝜑⋀⋀𝜑𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 5446, 5447
5449	→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 5443, 5448
5450	→→¬→𝜑⋀⋀𝜑𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
5451	→→¬→𝜑⋀⋀𝜑𝜓𝜒→𝜓¬𝜒→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒	Modus ponens 5449, 5450
5452	→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒	Modus ponens 5415, 5451
5453	→→¬→𝜑⋀⋀𝜑𝜓𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3
5454	→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5452, 5453
5455	→↔⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into biimp
5456	→⋀𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5013, 5455
5457	→→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5458	→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5454, 5457
5459	→→⋀𝜓𝜒→¬→𝜓¬𝜒→𝜑⋀⋀𝜑𝜓𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5460	→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5458, 5459
5461	→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5456, 5460
5462	→𝜑→⋀𝜓𝜒𝜑	Subs [𝜓↗⋀𝜓𝜒] into ax-1
5463	→→𝜑→⋀𝜓𝜒𝜑→𝜑→𝜑→⋀𝜓𝜒𝜑	Subs [𝜑↗→𝜑→⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1
5464	→𝜑→𝜑→⋀𝜓𝜒𝜑	Modus ponens 5462, 5463
5465	→→𝜑→𝜑→⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→⋀𝜓𝜒𝜑	Subs [𝜓↗𝜑, 𝜒↗→⋀𝜓𝜒𝜑] into ax-2
5466	→→𝜑𝜑→𝜑→⋀𝜓𝜒𝜑	Modus ponens 5464, 5465
5467	→→⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5468	→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5461, 5467
5469	→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5470	→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5468, 5469
5471	→→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5472	→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5470, 5471
5473	→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5462, 5472
5474	→¬¬⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒] into notnotr
5475	→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
5476	→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 5001, 5475
5477	→→¬¬⋀𝜓𝜒→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→¬¬⋀𝜓𝜒⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5478	→→¬¬⋀𝜓𝜒⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 5476, 5477
5479	→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 5474, 5478
5480	→→𝜑→⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5481	→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5473, 5480
5482	→→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
5483	→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5481, 5482
5484	→→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑⋀⋀𝜑𝜓𝜒] into ax-2
5485	→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5483, 5484
5486	→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 5479, 5485
5487	→𝜑→¬¬⋀𝜓𝜒𝜑	Subs [𝜓↗¬¬⋀𝜓𝜒] into ax-1
5488	→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑	Subs [𝜑↗→𝜑→¬¬⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1
5489	→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑	Modus ponens 5487, 5488
5490	→→𝜑→𝜑→¬¬⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→¬¬⋀𝜓𝜒𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜑] into ax-2
5491	→→𝜑𝜑→𝜑→¬¬⋀𝜓𝜒𝜑	Modus ponens 5489, 5490
5492	→→¬¬⋀𝜓𝜒→𝜑⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5493	→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5486, 5492
5494	→→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5495	→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5493, 5494
5496	→→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒] into ax-2
5497	→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5495, 5496
5498	→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5487, 5497
5499	→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒] into notnot
5500	→→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
5501	→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Modus ponens 5499, 5500
5502	→→¬¬⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗¬¬⋀⋀𝜑𝜓𝜒] into ax-2
5503	→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Modus ponens 5501, 5502
5504	→→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5505	→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Modus ponens 5503, 5504
5506	→→𝜑→→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Subs [𝜓↗→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒] into ax-2
5507	→→𝜑→¬¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Modus ponens 5505, 5506
5508	→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒	Modus ponens 5498, 5507
5509	→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-3
5510	→→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5511	→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒	Modus ponens 5509, 5510
5512	→→𝜑→→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒	Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒] into ax-2
5513	→→𝜑→¬¬⋀𝜓𝜒¬¬⋀⋀𝜑𝜓𝜒→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒	Modus ponens 5511, 5512
5514	→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒	Modus ponens 5508, 5513
5515	→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒] into id
5516	→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
5517	→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5518	→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒	Modus ponens 5516, 5517
5519	→→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑¬⋀⋀𝜑𝜓𝜒] into ax-2
5520	→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒	Modus ponens 5518, 5519
5521	→→𝜑→¬⋀⋀𝜑𝜓𝜒¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗¬⋀𝜓𝜒] into ax-2
5522	→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 5514, 5521
5523	→→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5524	→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 5522, 5523
5525	→→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜑¬⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
5526	→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 5524, 5525
5527	→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 5516, 5526
5528	→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒] into id
5529	→→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5530	→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5528, 5529
5531	→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒] into notnotr
5532	→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5533	→→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
5534	→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5532, 5533
5535	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
5536	→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5534, 5535
5537	→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5531, 5536
5538	→→¬⋀⋀𝜑𝜓𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
5539	→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5530, 5538
5540	→→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
5541	→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5539, 5540
5542	→→¬¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
5543	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5541, 5542
5544	→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
5545	→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5546	→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒	Modus ponens 5544, 5545
5547	→→¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒] into ax-2
5548	→→¬⋀⋀𝜑𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒	Modus ponens 5546, 5547
5549	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
5550	→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5537, 5549
5551	→→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5552	→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5550, 5551
5553	→→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
5554	→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬⋀⋀𝜑𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5552, 5553
5555	→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5544, 5554
5556	→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into ax-3
5557	→→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀⋀𝜑𝜓𝜒] into ax-1
5558	→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 5556, 5557
5559	→→¬⋀⋀𝜑𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2
5560	→→¬⋀⋀𝜑𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 5558, 5559
5561	→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 5555, 5560
5562	→→¬⋀⋀𝜑𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2
5563	→→¬⋀⋀𝜑𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 5561, 5562
5564	→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 5527, 5563
5565	→→¬⋀⋀𝜑𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3
5566	→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5564, 5565
5567	→↔⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into biimp
5568	→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 4981, 5567
5569	→→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
5570	→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5566, 5569
5571	→→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
5572	→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5570, 5571
5573	→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5568, 5572
5574	→→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi
5575	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5253, 5574
5576	↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 5573, 5575	anass
5577	→→⋀𝜑𝜓⋀𝜑𝜓→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-1
5578	→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 4647, 5577
5579	→→¬→𝜑¬𝜓→⋀𝜑𝜓⋀𝜑𝜓→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜓] into ax-2
5580	→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 5578, 5579
5581	→→¬→𝜑¬𝜓⋀𝜑𝜓→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗→¬→𝜑¬𝜓⋀𝜑𝜓] into ax-1
5582	→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 4661, 5581
5583	→→𝜓→¬→𝜑¬𝜓⋀𝜑𝜓→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜑𝜓] into ax-2
5584	→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓	Modus ponens 5582, 5583
5585	→→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓	Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
5586	→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓	Modus ponens 5584, 5585
5587	→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓⋀𝜑𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓⋀𝜑𝜓	Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓⋀𝜑𝜓] into ax-2
5588	→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓⋀𝜑𝜓	Modus ponens 5586, 5587
5589	→𝜑→𝜓⋀𝜑𝜓	Modus ponens pm3.2im, 5588	pm3.2
5590	→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into pm3.2
5591	→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
5592	→𝜑→𝜓→𝜒⋀𝜓𝜒	Modus ponens 5590, 5591
5593	→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Subs [𝜒↗→𝜒⋀𝜓𝜒] into ax-2
5594	→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 5592, 5593
5595	→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜓↗𝜒, 𝜒↗⋀𝜓𝜒] into ax-2
5596	→→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5597	→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5595, 5596
5598	→→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
5599	→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5597, 5598
5600	→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5594, 5599	pm3.43i
5601	↔⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into df-an
5602	→¬¬→𝜑𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜒] into notnotr
5603	→→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
5604	→→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1
5605	→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 5603, 5604
5606	→→¬¬→𝜑𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜑𝜒→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
5607	→→¬¬→𝜑𝜒→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 5605, 5606
5608	→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 5602, 5607
5609	→→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5610	→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens pm3.43i, 5609
5611	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1
5612	→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 5610, 5611
5613	→→¬¬→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
5614	→→¬¬→𝜑𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 5612, 5613
5615	→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 5608, 5614
5616	→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜑𝜒] into ax-1
5617	→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
5618	→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓	Modus ponens 5616, 5617
5619	→→→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜒→𝜑𝜓] into ax-2
5620	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓	Modus ponens 5618, 5619
5621	→→¬¬→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5622	→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5615, 5621
5623	→→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5624	→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5622, 5623
5625	→→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
5626	→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5624, 5625
5627	→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5616, 5626
5628	→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒] into notnot
5629	→→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒, 𝜓↗¬¬→𝜑𝜒] into ax-1
5630	→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒	Modus ponens 5628, 5629
5631	→→¬¬→𝜑𝜒→→𝜑⋀𝜓𝜒¬¬→𝜑⋀𝜓𝜒→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗¬¬→𝜑⋀𝜓𝜒] into ax-2
5632	→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒	Modus ponens 5630, 5631
5633	→→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒	Subs [𝜑↗→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5634	→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒	Modus ponens 5632, 5633
5635	→→→𝜑𝜓→→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜒↗→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒] into ax-2
5636	→→→𝜑𝜓→¬¬→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒	Modus ponens 5634, 5635
5637	→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒	Modus ponens 5627, 5636
5638	→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-3
5639	→→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
5640	→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒	Modus ponens 5638, 5639
5641	→→→𝜑𝜓→→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒] into ax-2
5642	→→→𝜑𝜓→¬¬→𝜑𝜒¬¬→𝜑⋀𝜓𝜒→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒	Modus ponens 5640, 5641
5643	→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒	Modus ponens 5637, 5642
5644	→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒] into id
5645	→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
5646	→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5647	→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒	Modus ponens 5645, 5646
5648	→→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓¬→𝜑⋀𝜓𝜒] into ax-2
5649	→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒	Modus ponens 5647, 5648
5650	→→→𝜑𝜓→¬→𝜑⋀𝜓𝜒¬→𝜑𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗¬→𝜑𝜒] into ax-2
5651	→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5643, 5650
5652	→→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5653	→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5651, 5652
5654	→→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓¬→𝜑𝜒] into ax-2
5655	→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5653, 5654
5656	→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5645, 5655
5657	→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒] into id
5658	→→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5659	→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5657, 5658
5660	→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒] into notnotr
5661	→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5662	→→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1
5663	→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5661, 5662
5664	→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5665	→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5663, 5664
5666	→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5660, 5665
5667	→→¬→𝜑⋀𝜓𝜒→¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5668	→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5659, 5667
5669	→→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1
5670	→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5668, 5669
5671	→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5672	→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5670, 5671
5673	→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-1
5674	→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5675	→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒	Modus ponens 5673, 5674
5676	→→¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒] into ax-2
5677	→→¬→𝜑⋀𝜓𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒	Modus ponens 5675, 5676
5678	→→¬¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5679	→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5666, 5678
5680	→→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5681	→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5679, 5680
5682	→→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5683	→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→𝜑⋀𝜓𝜒→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5681, 5682
5684	→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5673, 5683
5685	→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒] into ax-3
5686	→→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑⋀𝜓𝜒] into ax-1
5687	→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5685, 5686
5688	→→¬→𝜑⋀𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5689	→→¬→𝜑⋀𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5687, 5688
5690	→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5684, 5689
5691	→→¬→𝜑⋀𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒, 𝜒↗¬¬→→𝜑𝜓¬→𝜑𝜒] into ax-2
5692	→→¬→𝜑⋀𝜓𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5690, 5691
5693	→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5656, 5692
5694	→→¬→𝜑⋀𝜓𝜒¬¬→→𝜑𝜓¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒] into ax-3
5695	→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5693, 5694
5696	→↔⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒] into biimp
5697	→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒	Modus ponens 5601, 5696
5698	→→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into ax-1
5699	→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5695, 5698
5700	→→⋀→𝜑𝜓→𝜑𝜒→¬→→𝜑𝜓¬→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
5701	→→⋀→𝜑𝜓→𝜑𝜒¬→→𝜑𝜓¬→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5699, 5700
5702	→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5697, 5701	pm3.43
5703	↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into df-an
5704	→↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑	Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into bicom1
5705	↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑	Modus ponens 5703, 5704
5706	→↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑	Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into biimp
5707	→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑	Modus ponens 5705, 5706
5708	→→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
5709	→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑	Modus ponens 5707, 5708
5710	→→↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗⋀→𝜑𝜓→𝜓𝜑] into ax-2
5711	→→↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑	Modus ponens 5709, 5710
5712	→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑	Modus ponens 1605, 5711
5713	→↔¬→→𝜑𝜓¬→𝜓𝜑⋀→𝜑𝜓→𝜓𝜑↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into bicom1
5714	→↔⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into biimp
5715	→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑	Modus ponens 5703, 5714
5716	→↔↔𝜑𝜓¬→→𝜑𝜓¬→𝜓𝜑↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑] into bicom1
5717	↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens dfbi1, 5716
5718	→↔¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜓↗↔𝜑𝜓] into biimp
5719	→→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into ax-1
5720	→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓	Modus ponens 1371, 5719
5721	→→⋀→𝜑𝜓→𝜓𝜑→¬→→𝜑𝜓¬→𝜓𝜑↔𝜑𝜓→→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜑, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
5722	→→⋀→𝜑𝜓→𝜓𝜑¬→→𝜑𝜓¬→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 5720, 5721
5723	→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 5715, 5722
5724	→→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into impbi
5725	→→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑	Modus ponens 5712, 5724
5726	↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑	Modus ponens 5723, 5725	dfbi2
5727	↔↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into dfbi2
5728	→↔↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓→↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑, 𝜓↗⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓] into biimp
5729	→↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 5727, 5728
5730	⋀→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→⋀→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens dfbi2, 5729	dfbi
5731	→→𝜑→𝜓𝜑→→𝜑𝜓→𝜑𝜑	Subs [𝜒↗𝜑] into ax-2
5732	→→→𝜑𝜓→𝜑𝜑→¬¬𝜓→→𝜑𝜓→𝜑𝜑	Subs [𝜑↗→→𝜑𝜓→𝜑𝜑, 𝜓↗¬¬𝜓] into ax-1
5733	→¬¬𝜓→→𝜑𝜓→𝜑𝜑	Modus ponens 1148, 5732
5734	→→¬¬𝜓→→𝜑𝜓→𝜑𝜑→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜑] into ax-2
5735	→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑𝜑	Modus ponens 5733, 5734
5736	→¬¬𝜓→𝜑𝜑	Modus ponens 575, 5735
5737	→→¬¬𝜓→𝜑𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
5738	→→¬¬𝜓𝜑→¬¬𝜓𝜑	Modus ponens 5736, 5737
5739	→→→¬¬𝜓𝜑→¬¬𝜓𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓𝜑, 𝜓↗𝜑] into ax-1
5740	→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑	Modus ponens 5738, 5739
5741	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜑	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓𝜑] into ax-2
5742	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓𝜑	Modus ponens 5740, 5741
5743	→→𝜑¬¬𝜑→¬¬𝜓→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜓] into ax-1
5744	→¬¬𝜓→𝜑¬¬𝜑	Modus ponens notnot, 5743
5745	→→¬¬𝜓→𝜑¬¬𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
5746	→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑	Modus ponens 5744, 5745
5747	→→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑, 𝜓↗𝜑] into ax-1
5748	→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑	Modus ponens 5746, 5747
5749	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬𝜑→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬𝜑	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓¬¬𝜑] into ax-2
5750	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬𝜑	Modus ponens 5748, 5749
5751	→𝜑→¬¬𝜓¬¬𝜑	Modus ponens 581, 5750
5752	→→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓, 𝜓↗𝜑] into ax-1
5753	→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓	Modus ponens 2033, 5752
5754	→→𝜑→→¬¬𝜓¬¬𝜑→¬𝜑¬𝜓→→𝜑→¬¬𝜓¬¬𝜑→𝜑→¬𝜑¬𝜓	Subs [𝜓↗→¬¬𝜓¬¬𝜑, 𝜒↗→¬𝜑¬𝜓] into ax-2
5755	→→𝜑→¬¬𝜓¬¬𝜑→𝜑→¬𝜑¬𝜓	Modus ponens 5753, 5754
5756	→𝜑→¬𝜑¬𝜓	Modus ponens 5751, 5755
5757	→→¬𝜑→𝜑¬𝜑→¬𝜑→¬𝜑→𝜑¬𝜑	Subs [𝜑↗→¬𝜑→𝜑¬𝜑, 𝜓↗¬𝜑] into ax-1
5758	→¬𝜑→¬𝜑→𝜑¬𝜑	Modus ponens 414, 5757
5759	→→¬𝜑→¬𝜑→𝜑¬𝜑→→¬𝜑¬𝜑→¬𝜑→𝜑¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→𝜑¬𝜑] into ax-2
5760	→→¬𝜑¬𝜑→¬𝜑→𝜑¬𝜑	Modus ponens 5758, 5759
5761	→→𝜑→¬𝜑¬𝜓→→𝜑¬𝜑→𝜑¬𝜓	Subs [𝜓↗¬𝜑, 𝜒↗¬𝜓] into ax-2
5762	→→𝜑¬𝜑→𝜑¬𝜓	Modus ponens 5756, 5761
5763	→→→𝜑¬𝜑→𝜑¬𝜓→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5764	→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓	Modus ponens 5762, 5763
5765	→→¬𝜑→→𝜑¬𝜑→𝜑¬𝜓→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜓] into ax-2
5766	→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜓	Modus ponens 5764, 5765
5767	→¬𝜑→𝜑¬𝜓	Modus ponens 414, 5766
5768	→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5769	→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 619, 5768
5770	→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5771	→→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5772	→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Modus ponens 5770, 5771
5773	→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬𝜑¬→𝜑¬𝜓] into ax-2
5774	→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Modus ponens 5772, 5773
5775	→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Modus ponens 622, 5774
5776	→→¬𝜑→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
5777	→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Modus ponens 5769, 5776
5778	→→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5779	→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Modus ponens 5777, 5778
5780	→→¬¬¬→𝜑¬𝜓→→¬𝜑¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬𝜑¬→𝜑¬𝜓, 𝜒↗→¬𝜑¬→𝜑¬𝜓] into ax-2
5781	→→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓	Modus ponens 5779, 5780
5782	→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
5783	→→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
5784	→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑	Modus ponens 5782, 5783
5785	→→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬𝜑] into ax-2
5786	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑	Modus ponens 5784, 5785
5787	→→¬¬¬→𝜑¬𝜓→¬𝜑¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜓] into ax-2
5788	→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5775, 5787
5789	→→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5790	→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5788, 5789
5791	→→¬𝜑→→¬¬¬→𝜑¬𝜓¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
5792	→→¬𝜑→¬¬¬→𝜑¬𝜓¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5790, 5791
5793	→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 5782, 5792
5794	→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬𝜑] into ax-1
5795	→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 647, 5794
5796	→→¬𝜑→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
5797	→→¬𝜑→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 5795, 5796
5798	→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 5793, 5797
5799	→→¬𝜑→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬𝜑→𝜑¬𝜓→¬𝜑¬¬→𝜑¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
5800	→→¬𝜑→𝜑¬𝜓→¬𝜑¬¬→𝜑¬𝜓	Modus ponens 5798, 5799
5801	→¬𝜑¬¬→𝜑¬𝜓	Modus ponens 5767, 5800
5802	→→¬𝜑¬¬→𝜑¬𝜓→¬→𝜑¬𝜓𝜑	Subs [𝜓↗¬→𝜑¬𝜓] into ax-3
5803	→→¬→𝜑¬𝜓𝜑→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑	Subs [𝜑↗→¬→𝜑¬𝜓𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
5804	→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑	Modus ponens 866, 5803
5805	→→⋀𝜑𝜓→¬→𝜑¬𝜓𝜑→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜑] into ax-2
5806	→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜑	Modus ponens 5804, 5805
5807	→⋀𝜑𝜓𝜑	Modus ponens 4842, 5806	simpl
5808	→→𝜓→𝜑𝜓→𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→𝜓→𝜑𝜓] into ax-1
5809	→𝜓→𝜓→𝜑𝜓	Modus ponens 208, 5808
5810	→→𝜓→𝜓→𝜑𝜓→→𝜓𝜓→𝜓→𝜑𝜓	Subs [𝜑↗𝜓, 𝜒↗→𝜑𝜓] into ax-2
5811	→→𝜓𝜓→𝜓→𝜑𝜓	Modus ponens 5809, 5810
5812	→→𝜑→𝜓𝜑→¬¬𝜑→𝜑→𝜓𝜑	Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗¬¬𝜑] into ax-1
5813	→¬¬𝜑→𝜑→𝜓𝜑	Modus ponens ax-1, 5812
5814	→→¬¬𝜑→𝜑→𝜓𝜑→→¬¬𝜑𝜑→¬¬𝜑→𝜓𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→𝜓𝜑] into ax-2
5815	→→¬¬𝜑𝜑→¬¬𝜑→𝜓𝜑	Modus ponens 5813, 5814
5816	→¬¬𝜑→𝜓𝜑	Modus ponens notnotr, 5815
5817	→→𝜓→𝜑𝜓→→𝜓𝜑→𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
5818	→→𝜓𝜑→𝜓𝜓	Modus ponens 208, 5817
5819	→→→𝜓𝜑→𝜓𝜓→¬¬𝜑→→𝜓𝜑→𝜓𝜓	Subs [𝜑↗→→𝜓𝜑→𝜓𝜓, 𝜓↗¬¬𝜑] into ax-1
5820	→¬¬𝜑→→𝜓𝜑→𝜓𝜓	Modus ponens 5818, 5819
5821	→→¬¬𝜑→→𝜓𝜑→𝜓𝜓→→¬¬𝜑→𝜓𝜑→¬¬𝜑→𝜓𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜓] into ax-2
5822	→→¬¬𝜑→𝜓𝜑→¬¬𝜑→𝜓𝜓	Modus ponens 5820, 5821
5823	→¬¬𝜑→𝜓𝜓	Modus ponens 5816, 5822
5824	→𝜓→¬¬𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗¬¬𝜑] into ax-1
5825	→→𝜓→¬¬𝜑𝜓→𝜓→𝜓→¬¬𝜑𝜓	Subs [𝜑↗→𝜓→¬¬𝜑𝜓] into ax-1
5826	→𝜓→𝜓→¬¬𝜑𝜓	Modus ponens 5824, 5825
5827	→→𝜓→𝜓→¬¬𝜑𝜓→→𝜓𝜓→𝜓→¬¬𝜑𝜓	Subs [𝜑↗𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2
5828	→→𝜓𝜓→𝜓→¬¬𝜑𝜓	Modus ponens 5826, 5827
5829	→→¬¬𝜑→𝜓𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓	Subs [𝜑↗¬¬𝜑, 𝜒↗𝜓] into ax-2
5830	→→¬¬𝜑𝜓→¬¬𝜑𝜓	Modus ponens 5823, 5829
5831	→→→¬¬𝜑𝜓→¬¬𝜑𝜓→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓	Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑𝜓] into ax-1
5832	→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓	Modus ponens 5830, 5831
5833	→→𝜓→→¬¬𝜑𝜓→¬¬𝜑𝜓→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑𝜓] into ax-2
5834	→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑𝜓	Modus ponens 5832, 5833
5835	→→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓] into ax-1
5836	→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 488, 5835
5837	→→𝜓→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
5838	→→𝜓→¬¬𝜑𝜓→𝜓→¬¬𝜑¬¬𝜓	Modus ponens 5836, 5837
5839	→𝜓→¬¬𝜑¬¬𝜓	Modus ponens 5824, 5838
5840	→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑] into ax-1
5841	→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Modus ponens 494, 5840
5842	→→𝜓→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→𝜓→¬¬𝜑¬¬𝜓→𝜓→¬𝜓¬𝜑	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
5843	→→𝜓→¬¬𝜑¬¬𝜓→𝜓→¬𝜓¬𝜑	Modus ponens 5841, 5842
5844	→𝜓→¬𝜓¬𝜑	Modus ponens 5839, 5843
5845	→¬𝜓→𝜓¬𝜓	Subs [𝜑↗¬𝜓] into ax-1
5846	→→¬𝜓→𝜓¬𝜓→¬𝜓→¬𝜓→𝜓¬𝜓	Subs [𝜑↗→¬𝜓→𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
5847	→¬𝜓→¬𝜓→𝜓¬𝜓	Modus ponens 5845, 5846
5848	→→¬𝜓→¬𝜓→𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→𝜓¬𝜓] into ax-2
5849	→→¬𝜓¬𝜓→¬𝜓→𝜓¬𝜓	Modus ponens 5847, 5848
5850	→→𝜓→¬𝜓¬𝜑→→𝜓¬𝜓→𝜓¬𝜑	Subs [𝜑↗𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
5851	→→𝜓¬𝜓→𝜓¬𝜑	Modus ponens 5844, 5850
5852	→→→𝜓¬𝜓→𝜓¬𝜑→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑	Subs [𝜑↗→→𝜓¬𝜓→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5853	→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑	Modus ponens 5851, 5852
5854	→→¬𝜓→→𝜓¬𝜓→𝜓¬𝜑→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜓, 𝜒↗→𝜓¬𝜑] into ax-2
5855	→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜑	Modus ponens 5853, 5854
5856	→¬𝜓→𝜓¬𝜑	Modus ponens 5845, 5855
5857	→¬→𝜓¬𝜑¬→𝜓¬𝜑	Subs [𝜑↗¬→𝜓¬𝜑] into id
5858	→→¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑	Subs [𝜑↗→¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5859	→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑	Modus ponens 5857, 5858
5860	→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Subs [𝜑↗¬→𝜓¬𝜑] into notnotr
5861	→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5862	→→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Subs [𝜑↗→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1
5863	→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Modus ponens 5861, 5862
5864	→→¬¬¬→𝜓¬𝜑→¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗¬→𝜓¬𝜑, 𝜒↗→¬𝜓¬→𝜓¬𝜑] into ax-2
5865	→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Modus ponens 5863, 5864
5866	→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Modus ponens 5860, 5865
5867	→→¬𝜓→¬→𝜓¬𝜑¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜓¬𝜑, 𝜒↗¬→𝜓¬𝜑] into ax-2
5868	→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Modus ponens 5859, 5867
5869	→→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Subs [𝜑↗→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1
5870	→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Modus ponens 5868, 5869
5871	→→¬¬¬→𝜓¬𝜑→→¬𝜓¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗→¬𝜓¬→𝜓¬𝜑, 𝜒↗→¬𝜓¬→𝜓¬𝜑] into ax-2
5872	→→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑	Modus ponens 5870, 5871
5873	→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜓¬𝜑] into ax-1
5874	→→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
5875	→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓	Modus ponens 5873, 5874
5876	→→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜑¬𝜓] into ax-2
5877	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓	Modus ponens 5875, 5876
5878	→→¬¬¬→𝜓¬𝜑→¬𝜓¬→𝜓¬𝜑→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Subs [𝜑↗¬¬¬→𝜓¬𝜑, 𝜓↗¬𝜓, 𝜒↗¬→𝜓¬𝜑] into ax-2
5879	→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Modus ponens 5866, 5878
5880	→→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Subs [𝜑↗→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5881	→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Modus ponens 5879, 5880
5882	→→¬𝜓→→¬¬¬→𝜓¬𝜑¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜑¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑] into ax-2
5883	→→¬𝜓→¬¬¬→𝜓¬𝜑¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Modus ponens 5881, 5882
5884	→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑	Modus ponens 5873, 5883
5885	→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑	Subs [𝜑↗¬¬→𝜓¬𝜑, 𝜓↗→𝜓¬𝜑] into ax-3
5886	→→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑	Subs [𝜑↗→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑, 𝜓↗¬𝜓] into ax-1
5887	→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑	Modus ponens 5885, 5886
5888	→→¬𝜓→→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→→𝜓¬𝜑¬¬→𝜓¬𝜑→→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑, 𝜒↗→→𝜓¬𝜑¬¬→𝜓¬𝜑] into ax-2
5889	→→¬𝜓→¬¬¬→𝜓¬𝜑¬→𝜓¬𝜑→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑	Modus ponens 5887, 5888
5890	→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑	Modus ponens 5884, 5889
5891	→→¬𝜓→→𝜓¬𝜑¬¬→𝜓¬𝜑→→¬𝜓→𝜓¬𝜑→¬𝜓¬¬→𝜓¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜑, 𝜒↗¬¬→𝜓¬𝜑] into ax-2
5892	→→¬𝜓→𝜓¬𝜑→¬𝜓¬¬→𝜓¬𝜑	Modus ponens 5890, 5891
5893	→¬𝜓¬¬→𝜓¬𝜑	Modus ponens 5856, 5892
5894	→→¬𝜓¬¬→𝜓¬𝜑→¬→𝜓¬𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜓¬𝜑] into ax-3
5895	→¬→𝜓¬𝜑𝜓	Modus ponens 5893, 5894
5896	→↔⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑¬→𝜓¬𝜑	Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑] into biimp
5897	→⋀𝜓𝜑¬→𝜓¬𝜑	Modus ponens 4864, 5896
5898	→→¬→𝜓¬𝜑𝜓→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓	Subs [𝜑↗→¬→𝜓¬𝜑𝜓, 𝜓↗⋀𝜓𝜑] into ax-1
5899	→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓	Modus ponens 5895, 5898
5900	→→⋀𝜓𝜑→¬→𝜓¬𝜑𝜓→→⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑𝜓	Subs [𝜑↗⋀𝜓𝜑, 𝜓↗¬→𝜓¬𝜑, 𝜒↗𝜓] into ax-2
5901	→→⋀𝜓𝜑¬→𝜓¬𝜑→⋀𝜓𝜑𝜓	Modus ponens 5899, 5900
5902	→⋀𝜓𝜑𝜓	Modus ponens 5897, 5901
5903	→→⋀𝜓𝜑𝜓→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓	Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗¬→𝜓¬𝜑] into ax-1
5904	→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓	Modus ponens 5902, 5903
5905	→→¬→𝜓¬𝜑→⋀𝜓𝜑𝜓→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑𝜓	Subs [𝜑↗¬→𝜓¬𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗𝜓] into ax-2
5906	→→¬→𝜓¬𝜑⋀𝜓𝜑→¬→𝜓¬𝜑𝜓	Modus ponens 5904, 5905
5907	→→¬→𝜓¬𝜑𝜓→𝜑→¬→𝜓¬𝜑𝜓	Subs [𝜑↗→¬→𝜓¬𝜑𝜓, 𝜓↗𝜑] into ax-1
5908	→𝜑→¬→𝜓¬𝜑𝜓	Modus ponens 5895, 5907
5909	→→𝜑→¬→𝜓¬𝜑𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓	Subs [𝜓↗¬→𝜓¬𝜑, 𝜒↗𝜓] into ax-2
5910	→→𝜑¬→𝜓¬𝜑→𝜑𝜓	Modus ponens 5908, 5909
5911	→→→𝜑¬→𝜓¬𝜑→𝜑𝜓→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑¬→𝜓¬𝜑→𝜑𝜓] into ax-1
5912	→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓	Modus ponens 5910, 5911
5913	→→𝜓→→𝜑¬→𝜓¬𝜑→𝜑𝜓→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑¬→𝜓¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
5914	→→𝜓→𝜑¬→𝜓¬𝜑→𝜓→𝜑𝜓	Modus ponens 5912, 5913
5915	→→→𝜓𝜑→𝜓𝜓→𝜑→→𝜓𝜑→𝜓𝜓	Subs [𝜑↗→→𝜓𝜑→𝜓𝜓, 𝜓↗𝜑] into ax-1
5916	→𝜑→→𝜓𝜑→𝜓𝜓	Modus ponens 5818, 5915
5917	→→𝜑→→𝜓𝜑→𝜓𝜓→→𝜑→𝜓𝜑→𝜑→𝜓𝜓	Subs [𝜓↗→𝜓𝜑, 𝜒↗→𝜓𝜓] into ax-2
5918	→→𝜑→𝜓𝜑→𝜑→𝜓𝜓	Modus ponens 5916, 5917
5919	→→¬→𝜑¬𝜓𝜓→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓	Subs [𝜑↗→¬→𝜑¬𝜓𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
5920	→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓	Modus ponens simprim, 5919
5921	→→⋀𝜑𝜓→¬→𝜑¬𝜓𝜓→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜓] into ax-2
5922	→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓𝜓	Modus ponens 5920, 5921
5923	→⋀𝜑𝜓𝜓	Modus ponens 4842, 5922	simpr
5924	→→𝜑𝜒→𝜑𝜒	Modus ponens 815, 2228
5925	→𝜑→→𝜑𝜒𝜑	Subs [𝜓↗→𝜑𝜒] into ax-1
5926	→→𝜑→→𝜑𝜒𝜑→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑	Subs [𝜑↗→𝜑→→𝜑𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
5927	→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑	Modus ponens 5925, 5926
5928	→→⋀𝜑𝜓→𝜑→→𝜑𝜒𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→→𝜑𝜒𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→→𝜑𝜒𝜑] into ax-2
5929	→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→→𝜑𝜒𝜑	Modus ponens 5927, 5928
5930	→⋀𝜑𝜓→→𝜑𝜒𝜑	Modus ponens simpl, 5929
5931	→→→𝜑𝜒→𝜑𝜒→→→𝜑𝜒𝜑→→𝜑𝜒𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗𝜑] into ax-2
5932	→→→𝜑𝜒𝜑→→𝜑𝜒𝜒	Modus ponens 5924, 5931
5933	→→→→𝜑𝜒𝜑→→𝜑𝜒𝜒→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒	Subs [𝜑↗→→→𝜑𝜒𝜑→→𝜑𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5934	→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒	Modus ponens 5932, 5933
5935	→→⋀𝜑𝜓→→→𝜑𝜒𝜑→→𝜑𝜒𝜒→→⋀𝜑𝜓→→𝜑𝜒𝜑→⋀𝜑𝜓→→𝜑𝜒𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→𝜑𝜒𝜑, 𝜒↗→→𝜑𝜒𝜒] into ax-2
5936	→→⋀𝜑𝜓→→𝜑𝜒𝜑→⋀𝜑𝜓→→𝜑𝜒𝜒	Modus ponens 5934, 5935
5937	→⋀𝜑𝜓→→𝜑𝜒𝜒	Modus ponens 5930, 5936
5938	→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5939	→→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜒] into ax-1
5940	→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒	Modus ponens 5938, 5939
5941	→→→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→⋀𝜑𝜓→𝜑𝜒] into ax-2
5942	→→→𝜑𝜒→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒	Modus ponens 5940, 5941
5943	→→⋀𝜑𝜓→→𝜑𝜒𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑𝜒] into ax-2
5944	→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒	Modus ponens 5937, 5943
5945	→→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑𝜒] into ax-1
5946	→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒	Modus ponens 5944, 5945
5947	→→→𝜑𝜒→→⋀𝜑𝜓→𝜑𝜒→⋀𝜑𝜓𝜒→→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗→⋀𝜑𝜓→𝜑𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
5948	→→→𝜑𝜒→⋀𝜑𝜓→𝜑𝜒→→𝜑𝜒→⋀𝜑𝜓𝜒	Modus ponens 5946, 5947
5949	→→𝜑𝜒→⋀𝜑𝜓𝜒	Modus ponens 5938, 5948	pm3.41
5950	→𝜓→𝜒𝜒	Modus ponens 209, 51
5951	→𝜓→→𝜓𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜓𝜒] into ax-1
5952	→→𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓	Subs [𝜑↗→𝜓→→𝜓𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
5953	→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓	Modus ponens 5951, 5952
5954	→→⋀𝜑𝜓→𝜓→→𝜓𝜒𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→→𝜓𝜒𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→→𝜓𝜒𝜓] into ax-2
5955	→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→→𝜓𝜒𝜓	Modus ponens 5953, 5954
5956	→⋀𝜑𝜓→→𝜓𝜒𝜓	Modus ponens simpr, 5955
5957	→→→𝜓𝜒→𝜓𝜒→→→𝜓𝜒𝜓→→𝜓𝜒𝜒	Subs [𝜑↗→𝜓𝜒] into ax-2
5958	→→→𝜓𝜒𝜓→→𝜓𝜒𝜒	Modus ponens 867, 5957
5959	→→→→𝜓𝜒𝜓→→𝜓𝜒𝜒→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒	Subs [𝜑↗→→→𝜓𝜒𝜓→→𝜓𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5960	→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒	Modus ponens 5958, 5959
5961	→→⋀𝜑𝜓→→→𝜓𝜒𝜓→→𝜓𝜒𝜒→→⋀𝜑𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→→𝜓𝜒𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→→𝜓𝜒𝜓, 𝜒↗→→𝜓𝜒𝜒] into ax-2
5962	→→⋀𝜑𝜓→→𝜓𝜒𝜓→⋀𝜑𝜓→→𝜓𝜒𝜒	Modus ponens 5960, 5961
5963	→⋀𝜑𝜓→→𝜓𝜒𝜒	Modus ponens 5956, 5962
5964	→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
5965	→→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
5966	→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒	Modus ponens 5964, 5965
5967	→→→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→⋀𝜑𝜓→𝜓𝜒] into ax-2
5968	→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒	Modus ponens 5966, 5967
5969	→→⋀𝜑𝜓→→𝜓𝜒𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-2
5970	→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 5963, 5969
5971	→→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
5972	→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 5970, 5971
5973	→→→𝜓𝜒→→⋀𝜑𝜓→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
5974	→→→𝜓𝜒→⋀𝜑𝜓→𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 5972, 5973
5975	→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 5964, 5974	pm3.42
5976	→↔𝜑⋀𝜓𝜒→⋀𝜓𝜒𝜑	Subs [𝜓↗⋀𝜓𝜒] into biimpr
5977	→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
5978	→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
5979	→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 5977, 5978
5980	→→⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒⋀𝜓𝜒] into ax-2
5981	→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 5979, 5980
5982	→→↔𝜑⋀𝜓𝜒→⋀𝜓𝜒𝜑→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜑] into ax-2
5983	→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5976, 5982
5984	→→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
5985	→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5983, 5984
5986	→→⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→↔𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2
5987	→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5985, 5986
5988	→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5977, 5987
5989	→→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗¬→𝜓¬𝜒] into ax-1
5990	→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5988, 5989
5991	→→¬→𝜓¬𝜒→⋀𝜓𝜒→↔𝜑⋀𝜓𝜒𝜑→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2
5992	→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5990, 5991
5993	→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5017, 5992
5994	→→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜒] into ax-1
5995	→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5993, 5994
5996	→→𝜒→¬→𝜓¬𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→↔𝜑⋀𝜓𝜒𝜑] into ax-2
5997	→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5995, 5996
5998	→→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-1
5999	→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5997, 5998
6000	→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-2
6001	→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5999, 6000
6002	→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 5023, 6001
6003	→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗𝜑] into pm2.27
6004	→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑] into ax-1
6005	→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑	Modus ponens 6003, 6004
6006	→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6007	→→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-1
6008	→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 6006, 6007
6009	→→𝜓→→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗𝜓, 𝜓↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑] into ax-2
6010	→→𝜓→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 6008, 6009
6011	→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑	Modus ponens 6002, 6010
6012	→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜑] into imim2
6013	→→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Subs [𝜑↗→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6014	→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Modus ponens 6012, 6013
6015	→→↔𝜑⋀𝜓𝜒→→→↔𝜑⋀𝜓𝜒𝜑𝜑→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→→↔𝜑⋀𝜓𝜒𝜑𝜑, 𝜒↗→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-2
6016	→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Modus ponens 6014, 6015
6017	→→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Subs [𝜑↗→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-1
6018	→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Modus ponens 6016, 6017
6019	→→𝜓→→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑] into ax-2
6020	→→𝜓→↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒𝜑𝜑→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Modus ponens 6018, 6019
6021	→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑	Modus ponens 6005, 6020
6022	→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→𝜒𝜑] into ax-2
6023	→→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑	Subs [𝜑↗→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-1
6024	→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑	Modus ponens 6022, 6023
6025	→→𝜓→→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑	Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑, 𝜒↗→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-2
6026	→→𝜓→↔𝜑⋀𝜓𝜒→→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜒𝜑→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑	Modus ponens 6024, 6025
6027	→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑	Modus ponens 6021, 6026
6028	→→𝜓→→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑	Subs [𝜑↗𝜓, 𝜓↗→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑, 𝜒↗→↔𝜑⋀𝜓𝜒→𝜒𝜑] into ax-2
6029	→→𝜓→↔𝜑⋀𝜓𝜒→𝜒→↔𝜑⋀𝜓𝜒𝜑→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑	Modus ponens 6027, 6028
6030	→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑	Modus ponens 6011, 6029
6031	→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜒] into id
6032	→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜒] into ax-1
6033	→→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6034	→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒	Modus ponens 6032, 6033
6035	→→↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑⋀𝜓𝜒] into ax-2
6036	→→↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒	Modus ponens 6034, 6035
6037	→→𝜓→↔𝜑⋀𝜓𝜒→𝜒𝜑→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑	Subs [𝜑↗𝜓, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜒𝜑] into ax-2
6038	→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑	Modus ponens 6030, 6037
6039	→→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑	Subs [𝜑↗→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6040	→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑	Modus ponens 6038, 6039
6041	→→↔𝜑⋀𝜓𝜒→→𝜓↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜓↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓→𝜒𝜑] into ax-2
6042	→→↔𝜑⋀𝜓𝜒→𝜓↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑	Modus ponens 6040, 6041
6043	→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑	Modus ponens 6032, 6042
6044	→𝜒→→𝜒𝜑𝜑	Subs [𝜑↗𝜒, 𝜓↗𝜑] into pm2.27
6045	→→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑	Subs [𝜑↗→𝜒→→𝜒𝜑𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6046	→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑	Modus ponens 6044, 6045
6047	→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑	Subs [𝜑↗→𝜓→𝜒𝜑, 𝜓↗𝜒] into ax-1
6048	→→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑	Subs [𝜑↗→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6049	→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑	Modus ponens 6047, 6048
6050	→→↔𝜑⋀𝜓𝜒→→𝜓→𝜒𝜑→𝜒→𝜓→𝜒𝜑→→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜓→𝜒𝜑, 𝜒↗→𝜒→𝜓→𝜒𝜑] into ax-2
6051	→→↔𝜑⋀𝜓𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑	Modus ponens 6049, 6050
6052	→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑	Modus ponens 6043, 6051
6053	→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑	Subs [𝜑↗→𝜒𝜑, 𝜓↗𝜑, 𝜒↗𝜓] into imim2
6054	→→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑	Subs [𝜑↗→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑, 𝜓↗𝜒] into ax-1
6055	→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑	Modus ponens 6053, 6054
6056	→→𝜒→→→𝜒𝜑𝜑→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑	Subs [𝜑↗𝜒, 𝜓↗→→𝜒𝜑𝜑, 𝜒↗→→𝜓→𝜒𝜑→𝜓𝜑] into ax-2
6057	→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑	Modus ponens 6055, 6056
6058	→→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑	Subs [𝜑↗→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6059	→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑	Modus ponens 6057, 6058
6060	→→↔𝜑⋀𝜓𝜒→→𝜒→→𝜒𝜑𝜑→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→→𝜒𝜑𝜑, 𝜒↗→𝜒→→𝜓→𝜒𝜑→𝜓𝜑] into ax-2
6061	→→↔𝜑⋀𝜓𝜒→𝜒→→𝜒𝜑𝜑→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑	Modus ponens 6059, 6060
6062	→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑	Modus ponens 6046, 6061
6063	→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑	Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒𝜑, 𝜒↗→𝜓𝜑] into ax-2
6064	→→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑	Subs [𝜑↗→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑, 𝜓↗↔𝜑⋀𝜓𝜒] into ax-1
6065	→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑	Modus ponens 6063, 6064
6066	→→↔𝜑⋀𝜓𝜒→→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→→𝜓→𝜒𝜑→𝜓𝜑, 𝜒↗→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑] into ax-2
6067	→→↔𝜑⋀𝜓𝜒→𝜒→→𝜓→𝜒𝜑→𝜓𝜑→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑	Modus ponens 6065, 6066
6068	→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑	Modus ponens 6062, 6067
6069	→→↔𝜑⋀𝜓𝜒→→𝜒→𝜓→𝜒𝜑→𝜒→𝜓𝜑→→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗→𝜒→𝜓→𝜒𝜑, 𝜒↗→𝜒→𝜓𝜑] into ax-2
6070	→→↔𝜑⋀𝜓𝜒→𝜒→𝜓→𝜒𝜑→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑	Modus ponens 6068, 6069
6071	→↔𝜑⋀𝜓𝜒→𝜒→𝜓𝜑	Modus ponens 6052, 6070	simplbi2comt
6072	→⋀𝜓𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜒] into simpl
6073	→→⋀𝜓𝜒𝜓→𝜑→⋀𝜓𝜒𝜓	Subs [𝜑↗→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
6074	→𝜑→⋀𝜓𝜒𝜓	Modus ponens 6072, 6073
6075	→→𝜑→⋀𝜓𝜒𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
6076	→→𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 6074, 6075
6077	→⋀𝜓𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into simpr
6078	→→⋀𝜓𝜒𝜒→𝜑→⋀𝜓𝜒𝜒	Subs [𝜑↗→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
6079	→𝜑→⋀𝜓𝜒𝜒	Modus ponens 6077, 6078
6080	→→𝜑→⋀𝜓𝜒𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒	Subs [𝜓↗⋀𝜓𝜒] into ax-2
6081	→→𝜑⋀𝜓𝜒→𝜑𝜒	Modus ponens 6079, 6080
6082	→→𝜑𝜓→→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into pm3.2
6083	→→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6084	→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 5603, 6083
6085	→→→𝜑⋀𝜓𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
6086	→→→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 6084, 6085
6087	→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 6081, 6086
6088	→→→𝜑𝜓→→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2
6089	→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6082, 6088
6090	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6091	→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6089, 6090
6092	→→→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into ax-2
6093	→→→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6091, 6092
6094	→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6087, 6093
6095	→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6096	→→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6097	→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 6095, 6096
6098	→→→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒→𝜑𝜓] into ax-2
6099	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 6097, 6098
6100	→→→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2
6101	→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6094, 6100
6102	→→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
6103	→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6101, 6102
6104	→→→𝜑𝜓→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒] into ax-2
6105	→→→𝜑𝜓→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6103, 6104
6106	→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6095, 6105
6107	→→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into ax-1
6108	→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6106, 6107
6109	→→→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒] into ax-2
6110	→→→𝜑⋀𝜓𝜒→𝜑𝜓→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6108, 6109
6111	→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6076, 6110
6112	→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒] into id
6113	→→→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into ax-2
6114	→→→𝜑⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6111, 6113
6115	→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6112, 6114
6116	→→→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒→→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into impbi
6117	→→⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6115, 6116
6118	↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒	Modus ponens pm3.43, 6117	jcab
6119	→↔→𝜑⋀𝜓𝜒⋀→𝜑𝜓→𝜑𝜒↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into bicom1
6120	↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens jcab, 6119	pm4.76
6121	→→⋀𝜓𝜑𝜓→𝜑→⋀𝜓𝜑𝜓	Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗𝜑] into ax-1
6122	→𝜑→⋀𝜓𝜑𝜓	Modus ponens 5902, 6121
6123	→→𝜓⋀𝜓𝜑→→⋀𝜓𝜑𝜓↔𝜓⋀𝜓𝜑	Subs [𝜑↗𝜓, 𝜓↗⋀𝜓𝜑] into impbi
6124	→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓	Subs [𝜑↗→⋀𝜓𝜑𝜓, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1
6125	→→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓	Subs [𝜑↗→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓, 𝜓↗𝜑] into ax-1
6126	→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓	Modus ponens 6124, 6125
6127	→→𝜑→→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓	Subs [𝜓↗→⋀𝜓𝜑𝜓, 𝜒↗→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓] into ax-2
6128	→→𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓	Modus ponens 6126, 6127
6129	→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓	Modus ponens 6122, 6128
6130	→→→𝜓⋀𝜓𝜑→→⋀𝜓𝜑𝜓↔𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑	Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→⋀𝜓𝜑𝜓, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2
6131	→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6123, 6130
6132	→→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑	Subs [𝜑↗→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6133	→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6131, 6132
6134	→→𝜑→→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑	Subs [𝜓↗→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓, 𝜒↗→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑] into ax-2
6135	→→𝜑→→𝜓⋀𝜓𝜑→⋀𝜓𝜑𝜓→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6133, 6134
6136	→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6129, 6135
6137	→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑	Subs [𝜑↗→𝜓⋀𝜓𝜑] into id
6138	→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑	Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6139	→→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑	Subs [𝜑↗→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1
6140	→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑	Modus ponens 6138, 6139
6141	→→→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑	Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗→𝜑→𝜓⋀𝜓𝜑] into ax-2
6142	→→→𝜓⋀𝜓𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑	Modus ponens 6140, 6141
6143	→→𝜑→→𝜓⋀𝜓𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2
6144	→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6136, 6143
6145	→→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜑↗→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗→𝜓⋀𝜓𝜑] into ax-1
6146	→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6144, 6145
6147	→→→𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜑↗→𝜓⋀𝜓𝜑, 𝜓↗→𝜑→𝜓⋀𝜓𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2
6148	→→→𝜓⋀𝜓𝜑→𝜑→𝜓⋀𝜓𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6146, 6147
6149	→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6138, 6148
6150	→→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜑↗→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6151	→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6149, 6150
6152	→→𝜑→→𝜓⋀𝜓𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜓⋀𝜓𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜓↗→𝜓⋀𝜓𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2
6153	→→𝜑→𝜓⋀𝜓𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6151, 6152
6154	→𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens pm3.21, 6153
6155	→→𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗↔𝜓⋀𝜓𝜑] into ax-2
6156	→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6154, 6155
6157	→→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜑↗→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗𝜑] into ax-1
6158	→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6156, 6157
6159	→→𝜑→→𝜑𝜑→𝜑↔𝜓⋀𝜓𝜑→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑	Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔𝜓⋀𝜓𝜑] into ax-2
6160	→→𝜑→𝜑𝜑→𝜑→𝜑↔𝜓⋀𝜓𝜑	Modus ponens 6158, 6159
6161	→𝜑↔𝜓⋀𝜓𝜑	Modus ponens id, 6156	iba
6162	↔⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜑] into ancom
6163	→↔⋀𝜓𝜑⋀𝜑𝜓→𝜑↔⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
6164	→𝜑↔⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6162, 6163
6165	↔→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑	Subs [𝜒↗⋀𝜓𝜑] into pm5.74
6166	→↔→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑	Subs [𝜑↗→𝜑↔𝜓⋀𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜓𝜑] into biimp
6167	→→𝜑↔𝜓⋀𝜓𝜑↔→𝜑𝜓→𝜑⋀𝜓𝜑	Modus ponens 6165, 6166
6168	↔→𝜑𝜓→𝜑⋀𝜓𝜑	Modus ponens iba, 6167	ancrb
6169	↔→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Subs [𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6170	→↔→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓] into biimp
6171	→→𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Modus ponens 6169, 6170
6172	↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Modus ponens 6164, 6171
6173	→↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6174	→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Modus ponens 6172, 6173
6175	→↔→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into biimp
6176	→→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6177	→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓	Modus ponens 6174, 6176
6178	→→→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2
6179	→→→𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 6177, 6178
6180	→→𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens ancr, 6179	ancl
6181	→↔→𝜑⋀𝜓𝜑→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑	Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1
6182	↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑	Modus ponens 6172, 6181
6183	→↔→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into biimp
6184	→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑	Modus ponens 6182, 6183
6185	→↔→𝜑𝜓→𝜑⋀𝜓𝜑↔→𝜑⋀𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑] into bicom1
6186	↔→𝜑⋀𝜓𝜑→𝜑𝜓	Modus ponens ancrb, 6185
6187	→↔→𝜑⋀𝜓𝜑→𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into biimp
6188	→→𝜑⋀𝜓𝜑→𝜑𝜓	Modus ponens 6186, 6187
6189	→→→𝜑⋀𝜓𝜑→𝜑𝜓→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜓𝜑→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into ax-1
6190	→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓	Modus ponens 6188, 6189
6191	→→→𝜑⋀𝜑𝜓→→𝜑⋀𝜓𝜑→𝜑𝜓→→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2
6192	→→→𝜑⋀𝜑𝜓→𝜑⋀𝜓𝜑→→𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6190, 6191
6193	→→𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6184, 6192
6194	→→→𝜑𝜓→𝜑⋀𝜑𝜓→→→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into impbi
6195	→→→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens ancl, 6194
6196	↔→𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 6193, 6195	anclb
6197	↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜒↗⋀𝜑𝜓] into pm5.74
6198	→↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜑𝜓] into bicom1
6199	↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓	Modus ponens 6197, 6198
6200	→↔↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓→↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜑⋀𝜑𝜓, 𝜓↗→𝜑↔𝜓⋀𝜑𝜓] into biimp
6201	→↔→𝜑𝜓→𝜑⋀𝜑𝜓→𝜑↔𝜓⋀𝜑𝜓	Modus ponens 6199, 6200
6202	→𝜑↔𝜓⋀𝜑𝜓	Modus ponens anclb, 6201	ibar
6203	→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into ibar
6204	→↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6205	→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens pm4.76, 6204
6206	↔→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗⋀→𝜑𝜓→𝜑𝜒] into pm5.74
6207	→↔→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒, 𝜓↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp
6208	→→→𝜑𝜓↔→𝜑𝜒⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6206, 6207
6209	↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6203, 6208
6210	↔→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into pm5.74
6211	→↔→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒] into biimp
6212	→→→𝜑𝜓↔⋀→𝜑𝜓→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 6210, 6211
6213	↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 6205, 6212
6214	→↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into biimp
6215	→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 6213, 6214
6216	→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp
6217	→→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into ax-1
6218	→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 6215, 6217
6219	→→→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
6220	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 6218, 6219
6221	→↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into bicom1
6222	↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6213, 6221
6223	→↔→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into biimp
6224	→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒	Modus ponens 6222, 6223
6225	→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒] into bicom1
6226	↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 6209, 6225
6227	→↔→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒] into biimp
6228	→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 6226, 6227
6229	→→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-1
6230	→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 6228, 6229
6231	→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
6232	→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀→𝜑𝜓→𝜑𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 6230, 6231
6233	→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 6224, 6232
6234	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into impbi
6235	→→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 5610, 6234
6236	↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 6233, 6235
6237	↔→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into pm5.74
6238	→↔→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒] into bicom1
6239	↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 6237, 6238
6240	→↔↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒] into biimp
6241	→↔→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 6239, 6240
6242	→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 6236, 6241	pm5.44
6243	↔↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑⋀𝜓𝜒] into bicom
6244	→↔↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗↔→𝜑⋀𝜓𝜒→𝜑𝜒] into biimp
6245	→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒	Modus ponens 6243, 6244
6246	→→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
6247	→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒	Modus ponens 6245, 6246
6248	→→→𝜑𝜓→↔→𝜑𝜒→𝜑⋀𝜓𝜒↔→𝜑⋀𝜓𝜒→𝜑𝜒→→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜒↗↔→𝜑⋀𝜓𝜒→𝜑𝜒] into ax-2
6249	→→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒	Modus ponens 6247, 6248
6250	→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒	Modus ponens pm5.44, 6249
6251	↔↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜒] into bicom
6252	→↔↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗↔→𝜑𝜒→𝜑⋀𝜓𝜒] into biimp
6253	→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 6251, 6252
6254	→→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6255	→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 6253, 6254
6256	→→→𝜑𝜓→↔→𝜑⋀𝜓𝜒→𝜑𝜒↔→𝜑𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜒↗↔→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
6257	→→→𝜑𝜓↔→𝜑⋀𝜓𝜒→𝜑𝜒→→𝜑𝜓↔→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 6255, 6256
6258	→𝜑↔𝜒⋀𝜑𝜒	Subs [𝜓↗𝜒] into ibar
6259	→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒	Subs [𝜑↗↔𝜒⋀𝜑𝜒] into ax-1
6260	→→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒	Subs [𝜑↗→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒, 𝜓↗𝜑] into ax-1
6261	→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒	Modus ponens 6259, 6260
6262	→→𝜑→↔𝜒⋀𝜑𝜒→𝜓↔𝜒⋀𝜑𝜒→→𝜑↔𝜒⋀𝜑𝜒→𝜑→𝜓↔𝜒⋀𝜑𝜒	Subs [𝜓↗↔𝜒⋀𝜑𝜒, 𝜒↗→𝜓↔𝜒⋀𝜑𝜒] into ax-2
6263	→→𝜑↔𝜒⋀𝜑𝜒→𝜑→𝜓↔𝜒⋀𝜑𝜒	Modus ponens 6261, 6262
6264	→𝜑→𝜓↔𝜒⋀𝜑𝜒	Modus ponens 6258, 6263
6265	↔→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74
6266	→↔→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜓↔𝜒⋀𝜑𝜒, 𝜓↗↔→𝜓𝜒→𝜓⋀𝜑𝜒] into biimp
6267	→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒	Modus ponens 6265, 6266
6268	→→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒	Subs [𝜑↗→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒, 𝜓↗𝜑] into ax-1
6269	→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒	Modus ponens 6267, 6268
6270	→→𝜑→→𝜓↔𝜒⋀𝜑𝜒↔→𝜓𝜒→𝜓⋀𝜑𝜒→→𝜑→𝜓↔𝜒⋀𝜑𝜒→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒	Subs [𝜓↗→𝜓↔𝜒⋀𝜑𝜒, 𝜒↗↔→𝜓𝜒→𝜓⋀𝜑𝜒] into ax-2
6271	→→𝜑→𝜓↔𝜒⋀𝜑𝜒→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒	Modus ponens 6269, 6270
6272	→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒	Modus ponens 6264, 6271
6273	↔→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒	Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓⋀𝜑𝜒] into pm5.74
6274	→↔→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒, 𝜓↗↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒] into biimp
6275	→→𝜑↔→𝜓𝜒→𝜓⋀𝜑𝜒↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒	Modus ponens 6273, 6274
6276	↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒	Modus ponens 6272, 6275	pm5.42
6277	→→𝜑→𝜓⋀𝜑𝜓→→𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜒↗⋀𝜑𝜓] into ax-2
6278	→↔→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜑⋀𝜑𝜓] into biimp
6279	→→𝜑↔𝜓⋀𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 6197, 6278
6280	→↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into biimp
6281	→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒	Modus ponens pm5.42, 6280	anc2l
6282	→𝜑→𝜒⋀𝜒𝜑	Subs [𝜓↗𝜒] into pm3.21
6283	→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑	Subs [𝜑↗→𝜒⋀𝜒𝜑] into ax-1
6284	→→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑	Subs [𝜑↗→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑, 𝜓↗𝜑] into ax-1
6285	→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑	Modus ponens 6283, 6284
6286	→→𝜑→→𝜒⋀𝜒𝜑→𝜓→𝜒⋀𝜒𝜑→→𝜑→𝜒⋀𝜒𝜑→𝜑→𝜓→𝜒⋀𝜒𝜑	Subs [𝜓↗→𝜒⋀𝜒𝜑, 𝜒↗→𝜓→𝜒⋀𝜒𝜑] into ax-2
6287	→→𝜑→𝜒⋀𝜒𝜑→𝜑→𝜓→𝜒⋀𝜒𝜑	Modus ponens 6285, 6286
6288	→𝜑→𝜓→𝜒⋀𝜒𝜑	Modus ponens 6282, 6287
6289	→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜒𝜑] into ax-2
6290	→→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑	Subs [𝜑↗→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑, 𝜓↗𝜑] into ax-1
6291	→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑	Modus ponens 6289, 6290
6292	→→𝜑→→𝜓→𝜒⋀𝜒𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→→𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑	Subs [𝜓↗→𝜓→𝜒⋀𝜒𝜑, 𝜒↗→→𝜓𝜒→𝜓⋀𝜒𝜑] into ax-2
6293	→→𝜑→𝜓→𝜒⋀𝜒𝜑→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑	Modus ponens 6291, 6292
6294	→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑	Modus ponens 6288, 6293
6295	→→𝜑→→𝜓𝜒→𝜓⋀𝜒𝜑→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜒𝜑	Subs [𝜓↗→𝜓𝜒, 𝜒↗→𝜓⋀𝜒𝜑] into ax-2
6296	→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜒𝜑	Modus ponens 6294, 6295	anc2r
6297	→→⋀𝜑𝜓𝜑↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Subs [𝜑↗→⋀𝜑𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into iba
6298	↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Modus ponens simpl, 6297
6299	↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Subs [𝜓↗⋀𝜑𝜓] into dfbi2
6300	→↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into bicom1
6301	↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓	Modus ponens 6299, 6300
6302	→↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓	Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6303	→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓	Modus ponens 6301, 6302
6304	→↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into biimp
6305	→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Modus ponens 6298, 6304
6306	→→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓	Subs [𝜑↗→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into ax-1
6307	→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓	Modus ponens 6303, 6306
6308	→→→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓→→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜒↗↔𝜑⋀𝜑𝜓] into ax-2
6309	→→→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6307, 6308
6310	→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6305, 6309
6311	→↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1
6312	→↔↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into biimp
6313	→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑	Modus ponens 6299, 6312
6314	→↔→𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑] into bicom1
6315	↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓	Modus ponens 6298, 6314
6316	→↔⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓	Subs [𝜑↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6317	→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓	Modus ponens 6315, 6316
6318	→→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓	Subs [𝜑↗→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1
6319	→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓	Modus ponens 6317, 6318
6320	→→↔𝜑⋀𝜑𝜓→⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2
6321	→→↔𝜑⋀𝜑𝜓⋀→𝜑⋀𝜑𝜓→⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 6319, 6320
6322	→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 6313, 6321
6323	→→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into impbi
6324	→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6310, 6323
6325	↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6322, 6324
6326	→↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6327	→↔→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6328	→→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6329	→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6310, 6328
6330	→→→𝜑𝜓→→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗↔𝜑⋀𝜑𝜓] into ax-2
6331	→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6329, 6330
6332	→→𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens ancl, 6331
6333	→↔→𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1
6334	↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 6325, 6333
6335	→↔↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
6336	→↔→𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1
6337	↔→𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens anclb, 6336
6338	→↔→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
6339	→→→𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1
6340	→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6193, 6339
6341	→→↔𝜑⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
6342	→→↔𝜑⋀𝜑𝜓→𝜑⋀𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6340, 6341
6343	→↔𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6322, 6342
6344	→→→𝜑𝜓↔𝜑⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into impbi
6345	→→↔𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6332, 6344
6346	↔→𝜑𝜓↔𝜑⋀𝜑𝜓	Modus ponens 6343, 6345	pm4.71
6347	→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓] into id
6348	→↔⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into ax-1
6349	→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑	Modus ponens ancom, 6348
6350	↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6351	→↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
6352	→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6350, 6351
6353	↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6347, 6352
6354	↔→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.74
6355	→↔→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into biimp
6356	→→↔𝜑⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6354, 6355
6357	↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6349, 6356
6358	→↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into biimp
6359	→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6357, 6358
6360	→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
6361	→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6353, 6360
6362	→→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓𝜑] into ax-1
6363	→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6359, 6362
6364	→→→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into ax-2
6365	→→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6363, 6364
6366	→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6361, 6365
6367	→↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into bicom1
6368	↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6357, 6367
6369	→↔→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
6370	→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6368, 6369
6371	→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓] into bicom1
6372	↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑	Modus ponens 6353, 6371
6373	→↔→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜑𝜓𝜑] into biimp
6374	→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑	Modus ponens 6372, 6373
6375	→→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑	Subs [𝜑↗→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into ax-1
6376	→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑	Modus ponens 6374, 6375
6377	→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→↔𝜑⋀𝜑𝜓𝜑→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔𝜑⋀𝜑𝜓𝜑] into ax-2
6378	→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜑𝜓→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑	Modus ponens 6376, 6377
6379	→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑	Modus ponens 6370, 6378
6380	→→→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into impbi
6381	→→→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6366, 6380
6382	↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Modus ponens 6379, 6381
6383	↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into pm5.74
6384	→↔→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑] into bicom1
6385	↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6383, 6384
6386	→↔↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑] into biimp
6387	→↔→↔𝜑⋀𝜑𝜓𝜑→↔𝜑⋀𝜑𝜓⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6385, 6386
6388	→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6382, 6387
6389	→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜑] into id
6390	→↔⋀𝜑𝜓⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓𝜑] into bicom1
6391	→↔⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1
6392	→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6162, 6391
6393	↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜑] into pm5.74
6394	→↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑, 𝜓↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp
6395	→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Modus ponens 6393, 6394
6396	↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Modus ponens 6389, 6395
6397	↔→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6398	→↔→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into biimp
6399	→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6397, 6398
6400	↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6392, 6399
6401	→↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into biimp
6402	→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6400, 6401
6403	→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp
6404	→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Modus ponens 6396, 6403
6405	→→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑𝜑] into ax-1
6406	→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6402, 6405
6407	→→→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜒↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into ax-2
6408	→→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6406, 6407
6409	→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6404, 6408
6410	→↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into bicom1
6411	↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Modus ponens 6400, 6410
6412	→↔→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into biimp
6413	→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑	Modus ponens 6411, 6412
6414	→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜓𝜑↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑] into bicom1
6415	↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑	Modus ponens 6396, 6414
6416	→↔→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑𝜑] into biimp
6417	→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑	Modus ponens 6415, 6416
6418	→→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑	Subs [𝜑↗→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into ax-1
6419	→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑	Modus ponens 6417, 6418
6420	→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→↔𝜑⋀𝜓𝜑𝜑→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑	Subs [𝜑↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜓𝜑, 𝜒↗→↔𝜑⋀𝜓𝜑𝜑] into ax-2
6421	→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑	Modus ponens 6419, 6420
6422	→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑	Modus ponens 6413, 6421
6423	→→→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜓𝜑𝜑, 𝜓↗→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into impbi
6424	→→→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑𝜑↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6409, 6423
6425	↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6422, 6424
6426	↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜑𝜓] into pm5.74
6427	→↔→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓, 𝜓↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓] into bicom1
6428	↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Modus ponens 6426, 6427
6429	→↔↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Subs [𝜑↗↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓] into biimp
6430	→↔→↔𝜑⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Modus ponens 6428, 6429
6431	→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Modus ponens 6425, 6430
6432	→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into impbi
6433	→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6388, 6432
6434	↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6431, 6433
6435	→↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
6436	→↔→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6437	→→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into ax-1
6438	→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6388, 6437
6439	→→→𝜑𝜓→↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑→→→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓, 𝜒↗↔𝜑⋀𝜓𝜑] into ax-2
6440	→→→𝜑𝜓↔𝜑⋀𝜑𝜓→→𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6438, 6439
6441	→→𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6332, 6440
6442	→↔↔𝜑⋀𝜑𝜓↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into bicom1
6443	↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Modus ponens 6434, 6442
6444	→↔↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓] into biimp
6445	→↔→𝜑𝜓↔𝜑⋀𝜑𝜓↔↔𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜑𝜓] into bicom1
6446	↔↔𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens pm4.71, 6445
6447	→↔↔𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
6448	→→↔𝜑⋀𝜑𝜓→𝜑𝜓→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1
6449	→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6343, 6448
6450	→→↔𝜑⋀𝜓𝜑→↔𝜑⋀𝜑𝜓→𝜑𝜓→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
6451	→→↔𝜑⋀𝜓𝜑↔𝜑⋀𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓	Modus ponens 6449, 6450
6452	→↔𝜑⋀𝜓𝜑→𝜑𝜓	Modus ponens 6431, 6451
6453	→→→𝜑𝜓↔𝜑⋀𝜓𝜑→→↔𝜑⋀𝜓𝜑→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into impbi
6454	→→↔𝜑⋀𝜓𝜑→𝜑𝜓↔→𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6441, 6453
6455	↔→𝜑𝜓↔𝜑⋀𝜓𝜑	Modus ponens 6452, 6454	pm4.71r
6456	↔→𝜑𝜑↔𝜑⋀𝜑𝜑	Subs [𝜓↗𝜑] into pm4.71
6457	→↔→𝜑𝜑↔𝜑⋀𝜑𝜑→→𝜑𝜑↔𝜑⋀𝜑𝜑	Subs [𝜑↗→𝜑𝜑, 𝜓↗↔𝜑⋀𝜑𝜑] into biimp
6458	→→𝜑𝜑↔𝜑⋀𝜑𝜑	Modus ponens 6456, 6457
6459	↔𝜑⋀𝜑𝜑	Modus ponens id, 6458	pm4.24
6460	→↔𝜑⋀𝜑𝜑↔⋀𝜑𝜑𝜑	Subs [𝜓↗⋀𝜑𝜑] into bicom1
6461	↔⋀𝜑𝜑𝜑	Modus ponens pm4.24, 6460	anidm
6462	↔⋀𝜓𝜓𝜓	Subs [𝜑↗𝜓] into anidm
6463	→↔⋀𝜓𝜓𝜓→𝜑↔⋀𝜓𝜓𝜓	Subs [𝜑↗↔⋀𝜓𝜓𝜓, 𝜓↗𝜑] into ax-1
6464	→𝜑↔⋀𝜓𝜓𝜓	Modus ponens 6462, 6463
6465	↔→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓	Subs [𝜓↗⋀𝜓𝜓, 𝜒↗𝜓] into pm5.74
6466	→↔→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓→→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓	Subs [𝜑↗→𝜑↔⋀𝜓𝜓𝜓, 𝜓↗↔→𝜑⋀𝜓𝜓→𝜑𝜓] into biimp
6467	→→𝜑↔⋀𝜓𝜓𝜓↔→𝜑⋀𝜓𝜓→𝜑𝜓	Modus ponens 6465, 6466
6468	↔→𝜑⋀𝜓𝜓→𝜑𝜓	Modus ponens 6464, 6467	anidmdbi
6469	↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒	Subs [𝜒↗⋀𝜑𝜒] into impexp
6470	→↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into bicom1
6471	↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6469, 6470
6472	→↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into biimp
6473	→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6471, 6472
6474	→→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into ax-1
6475	→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6473, 6474
6476	→→→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒→→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒, 𝜒↗→⋀𝜑𝜓⋀𝜑𝜒] into ax-2
6477	→→→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6475, 6476
6478	→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens anc2l, 6477
6479	→↔→𝜑→𝜓⋀𝜑𝜒→⋀𝜑𝜓⋀𝜑𝜒↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into bicom1
6480	→↔→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒	Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into biimp
6481	→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒	Modus ponens 6469, 6480
6482	→↔→𝜑→𝜓𝜒→𝜑→𝜓⋀𝜑𝜒↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒] into bicom1
6483	↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Modus ponens pm5.42, 6482
6484	→↔→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓𝜒] into biimp
6485	→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 6483, 6484
6486	→→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6487	→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 6485, 6486
6488	→→→⋀𝜑𝜓⋀𝜑𝜒→→𝜑→𝜓⋀𝜑𝜒→𝜑→𝜓𝜒→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑→𝜓⋀𝜑𝜒, 𝜒↗→𝜑→𝜓𝜒] into ax-2
6489	→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓⋀𝜑𝜒→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 6487, 6488
6490	→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒	Modus ponens 6481, 6489
6491	→→→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓⋀𝜑𝜒] into impbi
6492	→→→⋀𝜑𝜓⋀𝜑𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6478, 6491
6493	↔→𝜑→𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6490, 6492	imdistan
6494	→→𝜑↔𝜒⋀𝜑𝜒→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒	Subs [𝜑↗→𝜑↔𝜒⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
6495	→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒	Modus ponens 6258, 6494
6496	→→⋀𝜑𝜓→𝜑↔𝜒⋀𝜑𝜒→→⋀𝜑𝜓𝜑→⋀𝜑𝜓↔𝜒⋀𝜑𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗↔𝜒⋀𝜑𝜒] into ax-2
6497	→→⋀𝜑𝜓𝜑→⋀𝜑𝜓↔𝜒⋀𝜑𝜒	Modus ponens 6495, 6496
6498	→⋀𝜑𝜓↔𝜒⋀𝜑𝜒	Modus ponens simpl, 6497
6499	↔→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74
6500	→↔→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒→→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→⋀𝜑𝜓↔𝜒⋀𝜑𝜒, 𝜓↗↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒] into biimp
6501	→→⋀𝜑𝜓↔𝜒⋀𝜑𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6499, 6500
6502	↔→⋀𝜑𝜓𝜒→⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6498, 6501	pm5.3
6503	↔↔𝜓𝜒↔¬𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into notbi
6504	→↔↔𝜓𝜒↔¬𝜓¬𝜒→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒	Subs [𝜑↗↔↔𝜓𝜒↔¬𝜓¬𝜒, 𝜓↗𝜑] into ax-1
6505	→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒	Modus ponens 6503, 6504
6506	↔→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜓↗↔𝜓𝜒, 𝜒↗↔¬𝜓¬𝜒] into pm5.74
6507	→↔→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒, 𝜓↗↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒] into biimp
6508	→→𝜑↔↔𝜓𝜒↔¬𝜓¬𝜒↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6506, 6507
6509	↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6505, 6508
6510	↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒	Subs [𝜓↗¬𝜓, 𝜒↗¬𝜒] into pm5.74
6511	↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→𝜑¬𝜓, 𝜓↗→𝜑¬𝜒] into notbi
6512	→↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6513	→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6511, 6512
6514	→↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒	Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into biimp
6515	→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒	Modus ponens 6510, 6514
6516	→→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into ax-1
6517	→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6513, 6516
6518	→→→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6519	→→→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6517, 6518
6520	→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6515, 6519
6521	→↔↔→𝜑¬𝜓→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒	Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6522	↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒	Modus ponens 6511, 6521
6523	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into biimp
6524	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒	Modus ponens 6522, 6523
6525	→↔→𝜑↔¬𝜓¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒] into bicom1
6526	↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6510, 6525
6527	→↔↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp
6528	→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6526, 6527
6529	→→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6530	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6528, 6529
6531	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔→𝜑¬𝜓→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔→𝜑¬𝜓→𝜑¬𝜒, 𝜒↗→𝜑↔¬𝜓¬𝜒] into ax-2
6532	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔→𝜑¬𝜓→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6530, 6531
6533	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6524, 6532
6534	→→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6535	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6520, 6534
6536	↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6533, 6535
6537	→↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6538	→↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp
6539	→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6509, 6538
6540	→→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
6541	→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6520, 6540
6542	→→→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6543	→→→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6541, 6542
6544	→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6539, 6543
6545	→↔→𝜑↔¬𝜓¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6546	↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Modus ponens 6536, 6545
6547	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into biimp
6548	→↔→𝜑↔𝜓𝜒→𝜑↔¬𝜓¬𝜒↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒] into bicom1
6549	↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒	Modus ponens 6509, 6548
6550	→↔→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔¬𝜓¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
6551	→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒	Modus ponens 6549, 6550
6552	→→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6553	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒	Modus ponens 6551, 6552
6554	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔¬𝜓¬𝜒→𝜑↔𝜓𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔¬𝜓¬𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
6555	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔¬𝜓¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Modus ponens 6553, 6554
6556	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Modus ponens 6533, 6555
6557	→→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6558	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6544, 6557
6559	↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6556, 6558
6560	↔⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜓↗𝜒] into df-an
6561	→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒] into id
6562	→↔⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6563	→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6560, 6562
6564	↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜒] into pm5.74
6565	→↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp
6566	→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Modus ponens 6564, 6565
6567	↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Modus ponens 6561, 6566
6568	↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜒, 𝜒↗¬→𝜑¬𝜒] into pm5.74
6569	→↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into biimp
6570	→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6568, 6569
6571	↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6563, 6570
6572	→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into biimp
6573	→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6571, 6572
6574	→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp
6575	→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Modus ponens 6567, 6574
6576	→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into ax-1
6577	→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6573, 6576
6578	→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜒↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into ax-2
6579	→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6577, 6578
6580	→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6575, 6579
6581	→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into bicom1
6582	↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Modus ponens 6571, 6581
6583	→↔→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into biimp
6584	→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒	Modus ponens 6582, 6583
6585	→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒] into bicom1
6586	↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Modus ponens 6567, 6585
6587	→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into biimp
6588	→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Modus ponens 6586, 6587
6589	→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Subs [𝜑↗→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into ax-1
6590	→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Modus ponens 6588, 6589
6591	→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒, 𝜒↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓] into ax-2
6592	→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Modus ponens 6590, 6591
6593	→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓	Modus ponens 6584, 6592
6594	→→→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into impbi
6595	→→→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6580, 6594
6596	↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6593, 6595
6597	↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜒] into pm5.74
6598	→↔→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒] into bicom1
6599	↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6597, 6598
6600	→↔↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6601	→↔→↔⋀𝜑𝜓⋀𝜑𝜒⋀𝜑𝜓→↔⋀𝜑𝜓⋀𝜑𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6599, 6600
6602	→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6596, 6601
6603	→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into id
6604	→↔⋀𝜑𝜒¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒] into bicom1
6605	↔¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6560, 6604
6606	→↔¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1
6607	→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6605, 6606
6608	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜒] into pm5.74
6609	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp
6610	→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 6608, 6609
6611	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 6603, 6610
6612	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜒] into pm5.74
6613	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into biimp
6614	→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6612, 6613
6615	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6607, 6614
6616	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into biimp
6617	→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6615, 6616
6618	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp
6619	→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 6611, 6618
6620	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1
6621	→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6617, 6620
6622	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into ax-2
6623	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6621, 6622
6624	→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6619, 6623
6625	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into bicom1
6626	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 6615, 6625
6627	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into biimp
6628	→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 6626, 6627
6629	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒] into bicom1
6630	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6611, 6629
6631	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6632	→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6630, 6631
6633	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into ax-1
6634	→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6632, 6633
6635	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓] into ax-2
6636	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6634, 6635
6637	→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6628, 6636
6638	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into impbi
6639	→→→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6624, 6638
6640	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6637, 6639
6641	↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜑𝜒] into pm5.74
6642	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒] into bicom1
6643	↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6641, 6642
6644	→↔↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒, 𝜓↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒] into biimp
6645	→↔→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6643, 6644
6646	→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6640, 6645
6647	→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into impbi
6648	→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6602, 6647
6649	↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6646, 6648
6650	↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒] into bicom
6651	→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into id
6652	→↔⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1
6653	→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens df-an, 6652
6654	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜓] into pm5.74
6655	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp
6656	→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6654, 6655
6657	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6651, 6656
6658	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗¬→𝜑¬𝜓] into pm5.74
6659	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into biimp
6660	→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6658, 6659
6661	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6653, 6660
6662	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into biimp
6663	→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6661, 6662
6664	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp
6665	→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6657, 6664
6666	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1
6667	→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6663, 6666
6668	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into ax-2
6669	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6667, 6668
6670	→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6665, 6669
6671	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into bicom1
6672	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6661, 6671
6673	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into biimp
6674	→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 6672, 6673
6675	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓] into bicom1
6676	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6657, 6675
6677	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6678	→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6676, 6677
6679	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into ax-1
6680	→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6678, 6679
6681	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓, 𝜒↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒] into ax-2
6682	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6680, 6681
6683	→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6674, 6682
6684	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into impbi
6685	→→→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6670, 6684
6686	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Modus ponens 6683, 6685
6687	↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜓] into pm5.74
6688	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓] into bicom1
6689	↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Modus ponens 6687, 6688
6690	→↔↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Subs [𝜑↗↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp
6691	→↔→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Modus ponens 6689, 6690
6692	→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Modus ponens 6686, 6691
6693	→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into id
6694	→↔¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into ax-1
6695	→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens pm4.63, 6694
6696	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜓] into pm5.74
6697	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp
6698	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 6696, 6697
6699	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 6693, 6698
6700	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗⋀𝜑𝜓] into pm5.74
6701	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into biimp
6702	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6700, 6701
6703	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6695, 6702
6704	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into biimp
6705	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6703, 6704
6706	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp
6707	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 6699, 6706
6708	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6709	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6705, 6708
6710	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into ax-2
6711	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6709, 6710
6712	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6707, 6711
6713	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into bicom1
6714	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 6703, 6713
6715	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into biimp
6716	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 6714, 6715
6717	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓] into bicom1
6718	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6699, 6717
6719	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6720	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6718, 6719
6721	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into ax-1
6722	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6720, 6721
6723	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6724	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6722, 6723
6725	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6716, 6724
6726	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into impbi
6727	→→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6712, 6726
6728	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Modus ponens 6725, 6727
6729	↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜒, 𝜒↗⋀𝜑𝜓] into pm5.74
6730	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓] into bicom1
6731	↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6729, 6730
6732	→↔↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓, 𝜓↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6733	→↔→↔¬→𝜑¬𝜒¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6731, 6732
6734	→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6728, 6733
6735	→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into impbi
6736	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Modus ponens 6692, 6735
6737	↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Modus ponens 6734, 6736
6738	↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜓] into bicom
6739	→↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6740	→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6738, 6739
6741	→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp
6742	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-1
6743	→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6740, 6742
6744	→→↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6745	→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6743, 6744
6746	→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6692, 6745
6747	→↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6748	↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Modus ponens 6738, 6747
6749	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into biimp
6750	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓	Modus ponens 6748, 6749
6751	→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓] into bicom1
6752	↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6737, 6751
6753	→↔↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6754	→→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6755	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6734, 6754
6756	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒¬→𝜑¬𝜓↔¬→𝜑¬𝜒⋀𝜑𝜓→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒¬→𝜑¬𝜓, 𝜒↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into ax-2
6757	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒¬→𝜑¬𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6755, 6756
6758	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6750, 6757
6759	→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6760	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6746, 6759
6761	↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6758, 6760
6762	→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6763	→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6764	→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6650, 6763
6765	→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-1
6766	→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6746, 6765
6767	→→↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6768	→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6766, 6767
6769	→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6764, 6768
6770	→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6771	↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Modus ponens 6761, 6770
6772	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into biimp
6773	→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓] into bicom1
6774	↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6650, 6773
6775	→↔↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6776	→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6774, 6775
6777	→→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6778	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6776, 6777
6779	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜒⋀𝜑𝜓↔⋀𝜑𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜒⋀𝜑𝜓, 𝜒↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into ax-2
6780	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜒⋀𝜑𝜓→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6778, 6779
6781	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6758, 6780
6782	→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6783	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6769, 6782
6784	↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6781, 6783
6785	→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6786	→↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6787	→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6788	→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6769, 6787
6789	→→↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜒↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-2
6790	→→↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6788, 6789
6791	→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6602, 6790
6792	→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6793	↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Modus ponens 6784, 6792
6794	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into biimp
6795	→↔↔⋀𝜑𝜓⋀𝜑𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒] into bicom1
6796	↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6649, 6795
6797	→↔↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into biimp
6798	→→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into ax-1
6799	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6646, 6798
6800	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓¬→𝜑¬𝜒, 𝜒↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-2
6801	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓¬→𝜑¬𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6799, 6800
6802	→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6781, 6801
6803	→→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into impbi
6804	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6791, 6803
6805	↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Modus ponens 6802, 6804
6806	→↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6807	↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6805, 6806
6808	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into biimp
6809	→↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6810	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗→𝜑↔𝜓𝜒] into ax-1
6811	→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6802, 6810
6812	→→→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜒↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-2
6813	→→→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6811, 6812
6814	→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6544, 6813
6815	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔⋀𝜑𝜓⋀𝜑𝜒↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into bicom1
6816	→↔↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into biimp
6817	→↔→𝜑↔𝜓𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒] into bicom1
6818	↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Modus ponens 6559, 6817
6819	→↔↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜓↗→𝜑↔𝜓𝜒] into biimp
6820	→→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into ax-1
6821	→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒	Modus ponens 6556, 6820
6822	→→↔⋀𝜑𝜓⋀𝜑𝜒→↔¬→𝜑¬𝜓¬→𝜑¬𝜒→𝜑↔𝜓𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗↔¬→𝜑¬𝜓¬→𝜑¬𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
6823	→→↔⋀𝜑𝜓⋀𝜑𝜒↔¬→𝜑¬𝜓¬→𝜑¬𝜒→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 6821, 6822
6824	→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 6791, 6823
6825	→→→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒→→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜑↔𝜓𝜒, 𝜓↗↔⋀𝜑𝜓⋀𝜑𝜒] into impbi
6826	→→↔⋀𝜑𝜓⋀𝜑𝜒→𝜑↔𝜓𝜒↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6814, 6825
6827	↔→𝜑↔𝜓𝜒↔⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 6824, 6826	pm5.32
6828	→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into idd
6829	→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6830	→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
6831	→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6829, 6830
6832	→→⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6833	→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6831, 6832
6834	→→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜓𝜒] into ax-2
6835	→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6828, 6834
6836	→→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
6837	→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6835, 6836
6838	→→⋀𝜓𝜒→→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6839	→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6837, 6838
6840	→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-1
6841	→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6829, 6840
6842	→→¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6843	→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6841, 6842
6844	→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 5017, 6843
6845	→→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6846	→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6844, 6845
6847	→→𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6848	→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6846, 6847
6849	→→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6850	→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6848, 6849
6851	→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6852	→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6850, 6851
6853	→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 5023, 6852
6854	→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into pm2.27
6855	→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒] into ax-1
6856	→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 6854, 6855
6857	→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6858	→→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6859	→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6857, 6858
6860	→→𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6861	→→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6859, 6860
6862	→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6853, 6861
6863	→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into imim2
6864	→→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6865	→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6863, 6864
6866	→→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6867	→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6865, 6866
6868	→→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-1
6869	→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6867, 6868
6870	→→𝜓→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6871	→→𝜓→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6869, 6870
6872	→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6856, 6871
6873	→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6874	→→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1
6875	→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6873, 6874
6876	→→𝜓→→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6877	→→𝜓→→𝜑𝜓→→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6875, 6876
6878	→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6872, 6877
6879	→→𝜓→→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6880	→→𝜓→→𝜑𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6878, 6879
6881	→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6862, 6880
6882	→→𝜑𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓] into ax-1
6883	→→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
6884	→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓	Modus ponens 6882, 6883
6885	→→→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓→𝜑𝜓] into ax-2
6886	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜑𝜓	Modus ponens 6884, 6885
6887	→→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6888	→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6881, 6887
6889	→→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6890	→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6888, 6889
6891	→→→𝜑𝜓→→𝜓→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜑𝜓, 𝜒↗→𝜓→𝜒⋀𝜓𝜒] into ax-2
6892	→→→𝜑𝜓→𝜓→𝜑𝜓→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6890, 6891
6893	→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6882, 6892
6894	→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗⋀𝜓𝜒] into pm2.27
6895	→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6896	→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 6894, 6895
6897	→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6898	→→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6899	→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6897, 6898
6900	→→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜓→𝜒⋀𝜓𝜒] into ax-2
6901	→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6899, 6900
6902	→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6893, 6901
6903	→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into imim2
6904	→→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6905	→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 6903, 6904
6906	→→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
6907	→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 6905, 6906
6908	→→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6909	→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 6907, 6908
6910	→→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
6911	→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 6909, 6910
6912	→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 6896, 6911
6913	→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
6914	→→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6915	→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6913, 6914
6916	→→→𝜑𝜓→→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2
6917	→→→𝜑𝜓→𝜒→→𝜓→𝜒⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6915, 6916
6918	→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6912, 6917
6919	→→→𝜑𝜓→→𝜒→𝜓→𝜒⋀𝜓𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2
6920	→→→𝜑𝜓→𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6918, 6919
6921	→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6902, 6920
6922	→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗⋀𝜓𝜒] into pm2.27
6923	→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6924	→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 6922, 6923
6925	→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜒→𝜓⋀𝜓𝜒] into ax-1
6926	→→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6927	→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6925, 6926
6928	→→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→𝜒→𝜓⋀𝜓𝜒] into ax-2
6929	→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6927, 6928
6930	→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6921, 6929
6931	→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into imim2
6932	→→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-1
6933	→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6931, 6932
6934	→→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6935	→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6933, 6934
6936	→→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6937	→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6935, 6936
6938	→→→𝜑𝜓→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒] into ax-2
6939	→→→𝜑𝜓→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6937, 6938
6940	→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒	Modus ponens 6924, 6939
6941	→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6942	→→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
6943	→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6941, 6942
6944	→→→𝜑𝜓→→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒] into ax-2
6945	→→→𝜑𝜓→𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6943, 6944
6946	→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6940, 6945
6947	→→→𝜑𝜓→→𝜓→𝜒→𝜓⋀𝜓𝜒→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→𝜒⋀𝜓𝜒] into ax-2
6948	→→→𝜑𝜓→𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6946, 6947
6949	→𝜓→→𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜑𝜓] into ax-1
6950	→→𝜓→→𝜑𝜓𝜓→𝜓→𝜓→→𝜑𝜓𝜓	Subs [𝜑↗→𝜓→→𝜑𝜓𝜓] into ax-1
6951	→𝜓→𝜓→→𝜑𝜓𝜓	Modus ponens 6949, 6950
6952	→→𝜓→𝜓→→𝜑𝜓𝜓→→𝜓𝜓→𝜓→→𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜒↗→→𝜑𝜓𝜓] into ax-2
6953	→→𝜓𝜓→𝜓→→𝜑𝜓𝜓	Modus ponens 6951, 6952
6954	→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜒↗→𝜒⋀𝜓𝜒] into ax-2
6955	→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6893, 6954
6956	→→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1
6957	→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6955, 6956
6958	→→𝜓→→→𝜑𝜓𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓𝜓→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓𝜓, 𝜒↗→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6959	→→𝜓→→𝜑𝜓𝜓→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6957, 6958
6960	→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒] into ax-1
6961	→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 6894, 6960
6962	→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6963	→→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-1
6964	→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6962, 6963
6965	→→𝜓→→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒] into ax-2
6966	→→𝜓→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6964, 6965
6967	→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒	Modus ponens 6881, 6966
6968	→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2
6969	→→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6970	→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6968, 6969
6971	→→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6972	→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6970, 6971
6973	→→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6974	→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6972, 6973
6975	→→𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6976	→→𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6974, 6975
6977	→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6961, 6976
6978	→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6979	→→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
6980	→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6978, 6979
6981	→→𝜓→→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6982	→→𝜓→𝜒→→→𝜑𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6980, 6981
6983	→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6977, 6982
6984	→→𝜓→→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
6985	→→𝜓→𝜒→→𝜑𝜓→𝜒⋀𝜓𝜒→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6983, 6984
6986	→→𝜒→𝜓𝜒→𝜒→𝜒→𝜓𝜒	Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗𝜒] into ax-1
6987	→𝜒→𝜒→𝜓𝜒	Modus ponens 5362, 6986
6988	→→𝜒→𝜒→𝜓𝜒→→𝜒𝜒→𝜒→𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2
6989	→→𝜒𝜒→𝜒→𝜓𝜒	Modus ponens 6987, 6988
6990	→→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
6991	→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6853, 6990
6992	→→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
6993	→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6991, 6992
6994	→→𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
6995	→→𝜒→𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6993, 6994
6996	→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 5362, 6995
6997	↔⋀𝜒𝜓¬→𝜒¬𝜓	Subs [𝜑↗𝜒] into df-an
6998	→→𝜓→𝜒𝜓→¬¬𝜓→𝜓→𝜒𝜓	Subs [𝜑↗→𝜓→𝜒𝜓, 𝜓↗¬¬𝜓] into ax-1
6999	→¬¬𝜓→𝜓→𝜒𝜓	Modus ponens 5350, 6998
7000	→→¬¬𝜓→𝜓→𝜒𝜓→→¬¬𝜓𝜓→¬¬𝜓→𝜒𝜓	Subs [𝜑↗¬¬𝜓, 𝜒↗→𝜒𝜓] into ax-2
7001	→→¬¬𝜓𝜓→¬¬𝜓→𝜒𝜓	Modus ponens 6999, 7000
7002	→¬¬𝜓→𝜒𝜓	Modus ponens 570, 7001
7003	→→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7004	→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6996, 7003
7005	→→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
7006	→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7004, 7005
7007	→→¬¬𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7008	→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7006, 7007
7009	→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7002, 7008
7010	→𝜒→¬¬𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗¬¬𝜓] into ax-1
7011	→→𝜒→¬¬𝜓𝜒→𝜒→𝜒→¬¬𝜓𝜒	Subs [𝜑↗→𝜒→¬¬𝜓𝜒, 𝜓↗𝜒] into ax-1
7012	→𝜒→𝜒→¬¬𝜓𝜒	Modus ponens 7010, 7011
7013	→→𝜒→𝜒→¬¬𝜓𝜒→→𝜒𝜒→𝜒→¬¬𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→¬¬𝜓𝜒] into ax-2
7014	→→𝜒𝜒→𝜒→¬¬𝜓𝜒	Modus ponens 7012, 7013
7015	→→¬¬𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7016	→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7009, 7015
7017	→→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7018	→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7016, 7017
7019	→→𝜒→→¬¬𝜓𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7020	→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7018, 7019
7021	→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7010, 7020
7022	→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒] into notnot
7023	→→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜓] into ax-1
7024	→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7022, 7023
7025	→→¬¬𝜓→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7026	→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7024, 7025
7027	→→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7028	→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7026, 7027
7029	→→𝜒→→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7030	→→𝜒→¬¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7028, 7029
7031	→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7021, 7030
7032	→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-3
7033	→→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓, 𝜓↗𝜒] into ax-1
7034	→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓	Modus ponens 7032, 7033
7035	→→𝜒→→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓] into ax-2
7036	→→𝜒→¬¬𝜓¬¬→→𝜑𝜓⋀𝜓𝜒→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓	Modus ponens 7034, 7035
7037	→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓	Modus ponens 7031, 7036
7038	→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒] into id
7039	→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7040	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7041	→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7039, 7040
7042	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7043	→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7041, 7042
7044	→→𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜓→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓	Subs [𝜑↗𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜓] into ax-2
7045	→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓	Modus ponens 7037, 7044
7046	→→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓	Subs [𝜑↗→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7047	→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓	Modus ponens 7045, 7046
7048	→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜒¬𝜓] into ax-2
7049	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓	Modus ponens 7047, 7048
7050	→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓	Modus ponens 7039, 7049
7051	→¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗¬→𝜒¬𝜓] into id
7052	→→¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗→¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7053	→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 7051, 7052
7054	→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗¬→𝜒¬𝜓] into notnotr
7055	→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7056	→→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Subs [𝜑↗→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
7057	→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Modus ponens 7055, 7056
7058	→→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓] into ax-2
7059	→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Modus ponens 7057, 7058
7060	→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Modus ponens 7054, 7059
7061	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓, 𝜒↗¬→𝜒¬𝜓] into ax-2
7062	→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Modus ponens 7053, 7061
7063	→→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
7064	→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Modus ponens 7062, 7063
7065	→→¬¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓] into ax-2
7066	→→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓	Modus ponens 7064, 7065
7067	→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
7068	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7069	→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7067, 7068
7070	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7071	→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7069, 7070
7072	→→¬¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜒¬𝜓] into ax-2
7073	→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 7060, 7072
7074	→→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7075	→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 7073, 7074
7076	→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓] into ax-2
7077	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 7075, 7076
7078	→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 7067, 7077
7079	→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓	Subs [𝜑↗¬¬→𝜒¬𝜓, 𝜓↗→𝜒¬𝜓] into ax-3
7080	→→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7081	→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓	Modus ponens 7079, 7080
7082	→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜒↗→→𝜒¬𝜓¬¬→𝜒¬𝜓] into ax-2
7083	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓	Modus ponens 7081, 7082
7084	→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓	Modus ponens 7078, 7083
7085	→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜒¬𝜓, 𝜒↗¬¬→𝜒¬𝜓] into ax-2
7086	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜒¬𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓	Modus ponens 7084, 7085
7087	→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓	Modus ponens 7050, 7086
7088	→→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-3
7089	→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7087, 7088
7090	→↔⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓¬→𝜒¬𝜓	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into biimp
7091	→⋀𝜒𝜓¬→𝜒¬𝜓	Modus ponens 6997, 7090
7092	→→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1
7093	→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7089, 7092
7094	→→⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7095	→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7093, 7094
7096	→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7091, 7095
7097	→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜒𝜓] into ax-1
7098	→→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
7099	→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓	Modus ponens 7097, 7098
7100	→→→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜒𝜓→𝜑𝜓] into ax-2
7101	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓	Modus ponens 7099, 7100
7102	→→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7103	→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒	Modus ponens 7096, 7102
7104	→→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒	Subs [𝜑↗→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7105	→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒	Modus ponens 7103, 7104
7106	→→→𝜑𝜓→→⋀𝜒𝜓→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜒𝜓→𝜑𝜓, 𝜒↗→⋀𝜒𝜓⋀𝜓𝜒] into ax-2
7107	→→→𝜑𝜓→⋀𝜒𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒	Modus ponens 7105, 7106
7108	→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒	Modus ponens 7097, 7107
7109	→⋀𝜒𝜓⋀𝜒𝜓	Subs [𝜑↗⋀𝜒𝜓] into id
7110	→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
7111	→→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓, 𝜓↗⋀𝜒𝜓] into ax-1
7112	→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓	Modus ponens 7110, 7111
7113	→→⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→→⋀𝜒𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜒𝜓] into ax-2
7114	→→⋀𝜒𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓	Modus ponens 7112, 7113
7115	→→→𝜑𝜓→⋀𝜒𝜓⋀𝜓𝜒→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7116	→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7108, 7115
7117	→→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1
7118	→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7116, 7117
7119	→→⋀𝜒𝜓→→→𝜑𝜓⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗→→𝜑𝜓⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7120	→→⋀𝜒𝜓→→𝜑𝜓⋀𝜒𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7118, 7119
7121	→↔⋀𝜒𝜓¬→𝜒¬𝜓↔¬→𝜒¬𝜓⋀𝜒𝜓	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into bicom1
7122	↔¬→𝜒¬𝜓⋀𝜒𝜓	Modus ponens 6997, 7121
7123	→↔¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓⋀𝜒𝜓	Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓] into biimp
7124	→¬→𝜒¬𝜓⋀𝜒𝜓	Modus ponens 7122, 7123
7125	→→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-1
7126	→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7096, 7125
7127	→→¬→𝜒¬𝜓→⋀𝜒𝜓→→𝜑𝜓⋀𝜓𝜒→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7128	→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7126, 7127
7129	→𝜒→𝜓¬→𝜒¬𝜓	Subs [𝜑↗𝜒] into pm3.2im
7130	→→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-1
7131	→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7089, 7130
7132	→→𝜓→¬→𝜒¬𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7133	→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7131, 7132
7134	→→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7135	→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7133, 7134
7136	→→𝜒→→𝜓¬→𝜒¬𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓¬→𝜒¬𝜓, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7137	→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7135, 7136
7138	→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7139	→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 6854, 7138
7140	→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7141	→→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7142	→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7140, 7141
7143	→→𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7144	→→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7142, 7143
7145	→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6996, 7144
7146	→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into imim2
7147	→→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7148	→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 7146, 7147
7149	→→→𝜑𝜓→→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
7150	→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 7148, 7149
7151	→→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7152	→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 7150, 7151
7153	→→𝜒→→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒] into ax-2
7154	→→𝜒→→𝜑𝜓→→→𝜑𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 7152, 7153
7155	→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒	Modus ponens 7139, 7154
7156	→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7157	→→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7158	→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7156, 7157
7159	→→𝜒→→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7160	→→𝜒→→𝜑𝜓→→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7158, 7159
7161	→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7155, 7160
7162	→→𝜒→→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7163	→→𝜒→→𝜑𝜓→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7161, 7162
7164	→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7145, 7163
7165	→→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7166	→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7164, 7165
7167	→→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7168	→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7166, 7167
7169	→→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2
7170	→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7168, 7169
7171	→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜒→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7172	→→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7173	→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7171, 7172
7174	→→→𝜑𝜓→→𝜒→𝜓⋀𝜓𝜒→𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2
7175	→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7173, 7174
7176	→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 6921, 7175
7177	→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7178	→→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7179	→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7177, 7178
7180	→→→𝜑𝜓→→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜒→𝜓⋀𝜓𝜒, 𝜒↗→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒] into ax-2
7181	→→→𝜑𝜓→𝜒→𝜒→𝜓⋀𝜓𝜒→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7179, 7180
7182	→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7176, 7181
7183	→→→𝜑𝜓→→𝜒𝜒→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜒, 𝜒↗→𝜒→𝜓⋀𝜓𝜒] into ax-2
7184	→→→𝜑𝜓→𝜒𝜒→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒	Modus ponens 7182, 7183
7185	→𝜒→→𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into ax-1
7186	→→𝜒→→𝜑𝜓𝜒→𝜒→𝜒→→𝜑𝜓𝜒	Subs [𝜑↗→𝜒→→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
7187	→𝜒→𝜒→→𝜑𝜓𝜒	Modus ponens 7185, 7186
7188	→→𝜒→𝜒→→𝜑𝜓𝜒→→𝜒𝜒→𝜒→→𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓𝜒] into ax-2
7189	→→𝜒𝜒→𝜒→→𝜑𝜓𝜒	Modus ponens 7187, 7188
7190	→→→𝜑𝜓→𝜒→𝜓⋀𝜓𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜓⋀𝜓𝜒] into ax-2
7191	→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 6921, 7190
7192	→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7193	→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7191, 7192
7194	→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7195	→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7193, 7194
7196	→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7197	→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 6922, 7196
7198	→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-1
7199	→→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7200	→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7198, 7199
7201	→→𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒] into ax-2
7202	→→𝜒→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7200, 7201
7203	→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒	Modus ponens 7164, 7202
7204	→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2
7205	→→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
7206	→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7204, 7205
7207	→→𝜓→→→𝜓⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7208	→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7206, 7207
7209	→→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7210	→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7208, 7209
7211	→→𝜒→→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7212	→→𝜒→𝜓→→𝜓⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7210, 7211
7213	→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7197, 7212
7214	→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7215	→→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7216	→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7214, 7215
7217	→→𝜒→→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7218	→→𝜒→𝜓→→→𝜑𝜓→𝜓⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7216, 7217
7219	→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7213, 7218
7220	→→𝜒→→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7221	→→𝜒→𝜓→→𝜑𝜓→𝜓⋀𝜓𝜒→𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7219, 7220
7222	→→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
7223	→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7004, 7222
7224	→→𝜓→→𝜒𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→𝜒𝜓→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7225	→→𝜓→𝜒𝜓→𝜓→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7223, 7224
7226	→→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
7227	→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6991, 7226
7228	→→¬¬𝜒→→𝜓𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓→→𝜑𝜓⋀𝜓𝜒] into ax-2
7229	→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7227, 7228
7230	→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒	Modus ponens 5367, 7229
7231	→→¬¬𝜒→𝜓→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7232	→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7230, 7231
7233	→→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-1
7234	→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7232, 7233
7235	→→𝜓→→¬¬𝜒𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7236	→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7234, 7235
7237	→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 5375, 7236
7238	→→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
7239	→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7022, 7238
7240	→→¬¬𝜒→→→𝜑𝜓⋀𝜓𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7241	→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7239, 7240
7242	→→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7243	→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7241, 7242
7244	→→𝜓→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7245	→→𝜓→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7243, 7244
7246	→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7237, 7245
7247	→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-3
7248	→→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-1
7249	→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Modus ponens 7247, 7248
7250	→→𝜓→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-2
7251	→→𝜓→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Modus ponens 7249, 7250
7252	→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Modus ponens 7246, 7251
7253	→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7254	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7255	→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7253, 7254
7256	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7257	→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7255, 7256
7258	→→𝜓→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2
7259	→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒	Modus ponens 7252, 7258
7260	→→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒	Subs [𝜑↗→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7261	→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒	Modus ponens 7259, 7260
7262	→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜓¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
7263	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒	Modus ponens 7261, 7262
7264	→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒	Modus ponens 7253, 7263
7265	→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7266	→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5416, 7265
7267	→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7268	→→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
7269	→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Modus ponens 7267, 7268
7270	→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒] into ax-2
7271	→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Modus ponens 7269, 7270
7272	→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Modus ponens 5419, 7271
7273	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
7274	→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Modus ponens 7266, 7273
7275	→→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
7276	→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Modus ponens 7274, 7275
7277	→→¬¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒] into ax-2
7278	→→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒	Modus ponens 7276, 7277
7279	→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
7280	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7281	→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7279, 7280
7282	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7283	→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7281, 7282
7284	→→¬¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
7285	→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 7272, 7284
7286	→→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7287	→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 7285, 7286
7288	→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
7289	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 7287, 7288
7290	→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 7279, 7289
7291	→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7292	→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 5444, 7291
7293	→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
7294	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 7292, 7293
7295	→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 7290, 7294
7296	→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
7297	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜓¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒	Modus ponens 7295, 7296
7298	→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒	Modus ponens 7264, 7297
7299	→→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3
7300	→→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
7301	→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 6844, 7300
7302	→→⋀𝜓𝜒→¬→𝜓¬𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7303	→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7301, 7302
7304	→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
7305	→→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
7306	→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓	Modus ponens 7304, 7305
7307	→→→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜓𝜒→𝜑𝜓] into ax-2
7308	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓	Modus ponens 7306, 7307
7309	→→⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7310	→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 6829, 7309
7311	→→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7312	→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 7310, 7311
7313	→→→𝜑𝜓→→⋀𝜓𝜒→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜓𝜒→𝜑𝜓, 𝜒↗→⋀𝜓𝜒⋀𝜓𝜒] into ax-2
7314	→→→𝜑𝜓→⋀𝜓𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 7312, 7313
7315	→→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7316	→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒	Modus ponens 5591, 7315
7317	→→→𝜑𝜓→→𝜓→𝜒⋀𝜓𝜒→𝜑→𝜓→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→𝜑→𝜓→𝜒⋀𝜓𝜒] into ax-2
7318	→→→𝜑𝜓→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒	Modus ponens 7316, 7317
7319	→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒	Modus ponens 6893, 7318
7320	→→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7321	→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 5593, 7320
7322	→→→𝜑𝜓→→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜓→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒] into ax-2
7323	→→→𝜑𝜓→𝜑→𝜓→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 7321, 7322
7324	→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 7319, 7323
7325	→→→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜓𝜒] into ax-2
7326	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 7324, 7325
7327	→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑→𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7328	→→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7329	→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒	Modus ponens 7327, 7328
7330	→→→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑→𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜑→𝜒⋀𝜓𝜒] into ax-2
7331	→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒	Modus ponens 7329, 7330
7332	→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒	Modus ponens 5594, 7331
7333	→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜑] into imim2
7334	→→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7335	→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 7333, 7334
7336	→→𝜒→→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒] into ax-2
7337	→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 7335, 7336
7338	→→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7339	→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 7337, 7338
7340	→→→𝜑𝜓→→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒] into ax-2
7341	→→→𝜑𝜓→𝜒→→𝜒⋀𝜓𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 7339, 7340
7342	→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 6896, 7341
7343	→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
7344	→→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7345	→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒	Modus ponens 7343, 7344
7346	→→→𝜑𝜓→→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜒↗→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒] into ax-2
7347	→→→𝜑𝜓→𝜒→→𝜑→𝜒⋀𝜓𝜒→𝜑⋀𝜓𝜒→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒	Modus ponens 7345, 7346
7348	→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒	Modus ponens 7342, 7347
7349	→→→𝜑𝜓→→𝜒→𝜑→𝜒⋀𝜓𝜒→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→𝜒→𝜑⋀𝜓𝜒] into ax-2
7350	→→→𝜑𝜓→𝜒→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒	Modus ponens 7348, 7349
7351	→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒	Modus ponens 7332, 7350
7352	→→→𝜑𝜓→𝜒→𝜑⋀𝜓𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
7353	→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 7351, 7352
7354	→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7355	→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 7353, 7354
7356	→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
7357	→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 7355, 7356
7358	→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 7185, 7357
7359	→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜓↗⋀𝜓𝜒] into pm2.27
7360	→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7361	→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒	Modus ponens 7359, 7360
7362	→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7363	→→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7364	→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 7362, 7363
7365	→→𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒] into ax-2
7366	→→𝜒→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 7364, 7365
7367	→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 7358, 7366
7368	→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into imim2
7369	→→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7370	→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7368, 7369
7371	→→𝜑→→→𝜑⋀𝜓𝜒⋀𝜓𝜒→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜓↗→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7372	→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7370, 7371
7373	→→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7374	→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7372, 7373
7375	→→𝜒→→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒, 𝜒↗→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7376	→→𝜒→𝜑→→𝜑⋀𝜓𝜒⋀𝜓𝜒→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7374, 7375
7377	→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7361, 7376
7378	→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Subs [𝜓↗→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7379	→→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜒] into ax-1
7380	→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7378, 7379
7381	→→𝜒→→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2
7382	→→𝜒→𝜑→→→𝜑𝜓→𝜑⋀𝜓𝜒→→𝜑𝜓⋀𝜓𝜒→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7380, 7381
7383	→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7377, 7382
7384	→→𝜒→→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒, 𝜒↗→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2
7385	→→𝜒→𝜑→→𝜑𝜓→𝜑⋀𝜓𝜒→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7383, 7384
7386	→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7367, 7385
7387	→→𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7388	→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7386, 7387
7389	→→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7390	→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7388, 7389
7391	→→𝜑→→𝜒𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→𝜒𝜑→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜓↗→𝜒𝜑, 𝜒↗→𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7392	→→𝜑→𝜒𝜑→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7390, 7391
7393	→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 13, 7392
7394	→→𝜒→𝜑𝜒→¬¬𝜒→𝜒→𝜑𝜒	Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗¬¬𝜒] into ax-1
7395	→¬¬𝜒→𝜒→𝜑𝜒	Modus ponens 1834, 7394
7396	→→¬¬𝜒→𝜒→𝜑𝜒→→¬¬𝜒𝜒→¬¬𝜒→𝜑𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
7397	→→¬¬𝜒𝜒→¬¬𝜒→𝜑𝜒	Modus ponens 7395, 7396
7398	→¬¬𝜒→𝜑𝜒	Modus ponens 5153, 7397
7399	→→𝜑→𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Subs [𝜓↗𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7400	→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7393, 7399
7401	→→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
7402	→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7400, 7401
7403	→→¬¬𝜒→→𝜑𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑→→𝜑𝜓⋀𝜓𝜒] into ax-2
7404	→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7402, 7403
7405	→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7398, 7404
7406	→𝜑→¬¬𝜒𝜑	Subs [𝜓↗¬¬𝜒] into ax-1
7407	→→𝜑→¬¬𝜒𝜑→𝜑→𝜑→¬¬𝜒𝜑	Subs [𝜑↗→𝜑→¬¬𝜒𝜑, 𝜓↗𝜑] into ax-1
7408	→𝜑→𝜑→¬¬𝜒𝜑	Modus ponens 7406, 7407
7409	→→𝜑→𝜑→¬¬𝜒𝜑→→𝜑𝜑→𝜑→¬¬𝜒𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬𝜒𝜑] into ax-2
7410	→→𝜑𝜑→𝜑→¬¬𝜒𝜑	Modus ponens 7408, 7409
7411	→→¬¬𝜒→𝜑→→𝜑𝜓⋀𝜓𝜒→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7412	→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7405, 7411
7413	→→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7414	→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7412, 7413
7415	→→𝜑→→¬¬𝜒𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒] into ax-2
7416	→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7414, 7415
7417	→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7406, 7416
7418	→→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7419	→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7241, 7418
7420	→→𝜑→→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜓↗→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7421	→→𝜑→¬¬𝜒→→𝜑𝜓⋀𝜓𝜒→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7419, 7420
7422	→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7417, 7421
7423	→→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒, 𝜓↗𝜑] into ax-1
7424	→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Modus ponens 7247, 7423
7425	→→𝜑→→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Subs [𝜓↗→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒] into ax-2
7426	→→𝜑→¬¬𝜒¬¬→→𝜑𝜓⋀𝜓𝜒→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Modus ponens 7424, 7425
7427	→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒	Modus ponens 7422, 7426
7428	→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
7429	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7430	→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7428, 7429
7431	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜑¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7432	→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7430, 7431
7433	→→𝜑→¬→→𝜑𝜓⋀𝜓𝜒¬𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒	Subs [𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬𝜒] into ax-2
7434	→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒	Modus ponens 7427, 7433
7435	→→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒	Subs [𝜑↗→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7436	→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒	Modus ponens 7434, 7435
7437	→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→𝜑¬𝜒] into ax-2
7438	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒	Modus ponens 7436, 7437
7439	→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒	Modus ponens 7428, 7438
7440	→¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬→𝜑¬𝜒] into id
7441	→→¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7442	→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 7440, 7441
7443	→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬→𝜑¬𝜒] into notnotr
7444	→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7445	→→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Subs [𝜑↗→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
7446	→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Modus ponens 7444, 7445
7447	→→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒] into ax-2
7448	→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Modus ponens 7446, 7447
7449	→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Modus ponens 7443, 7448
7450	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2
7451	→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Modus ponens 7442, 7450
7452	→→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Subs [𝜑↗→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
7453	→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Modus ponens 7451, 7452
7454	→→¬¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒, 𝜒↗→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒] into ax-2
7455	→→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒	Modus ponens 7453, 7454
7456	→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
7457	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7458	→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7456, 7457
7459	→→¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒] into ax-2
7460	→→¬→→𝜑𝜓⋀𝜓𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7458, 7459
7461	→→¬¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2
7462	→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 7449, 7461
7463	→→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7464	→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 7462, 7463
7465	→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒] into ax-2
7466	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→→𝜑𝜓⋀𝜓𝜒→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 7464, 7465
7467	→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 7456, 7466
7468	→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Subs [𝜑↗¬¬→𝜑¬𝜒, 𝜓↗→𝜑¬𝜒] into ax-3
7469	→→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒, 𝜓↗¬→→𝜑𝜓⋀𝜓𝜒] into ax-1
7470	→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Modus ponens 7468, 7469
7471	→→¬→→𝜑𝜓⋀𝜓𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→→𝜑¬𝜒¬¬→𝜑¬𝜒] into ax-2
7472	→→¬→→𝜑𝜓⋀𝜓𝜒→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Modus ponens 7470, 7471
7473	→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Modus ponens 7467, 7472
7474	→→¬→→𝜑𝜓⋀𝜓𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒	Subs [𝜑↗¬→→𝜑𝜓⋀𝜓𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗¬¬→𝜑¬𝜒] into ax-2
7475	→→¬→→𝜑𝜓⋀𝜓𝜒→𝜑¬𝜒→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒	Modus ponens 7473, 7474
7476	→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒	Modus ponens 7439, 7475
7477	→→¬→→𝜑𝜓⋀𝜓𝜒¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓⋀𝜓𝜒, 𝜓↗¬→𝜑¬𝜒] into ax-3
7478	→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7476, 7477
7479	→↔⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒¬→𝜑¬𝜒	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒] into biimp
7480	→⋀𝜑𝜒¬→𝜑¬𝜒	Modus ponens 6560, 7479
7481	→→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒, 𝜓↗⋀𝜑𝜒] into ax-1
7482	→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7478, 7481
7483	→→⋀𝜑𝜒→¬→𝜑¬𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→→𝜑𝜓⋀𝜓𝜒] into ax-2
7484	→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7482, 7483
7485	→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒	Modus ponens 7480, 7484
7486	→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀𝜑𝜒] into ax-1
7487	→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
7488	→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓	Modus ponens 7486, 7487
7489	→→→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒→𝜑𝜓] into ax-2
7490	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓	Modus ponens 7488, 7489
7491	→→⋀𝜑𝜒→→𝜑𝜓⋀𝜓𝜒→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗⋀𝜓𝜒] into ax-2
7492	→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 7485, 7491
7493	→→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
7494	→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 7492, 7493
7495	→→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜒] into ax-2
7496	→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 7494, 7495
7497	→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 7486, 7496	pm3.45
7498	↔→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.32
7499	→↔→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜒↔𝜑𝜓, 𝜓↗↔⋀𝜒𝜑⋀𝜒𝜓] into biimp
7500	→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Modus ponens 7498, 7499
7501	→→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Subs [𝜑↗→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
7502	→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Modus ponens 7500, 7501
7503	→→↔𝜑𝜓→→𝜒↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→𝜒↔𝜑𝜓, 𝜒↗↔⋀𝜒𝜑⋀𝜒𝜓] into ax-2
7504	→→↔𝜑𝜓→𝜒↔𝜑𝜓→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Modus ponens 7502, 7503
7505	→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓	Modus ponens 2521, 7504	anbi2
7506	↔⋀𝜑𝜒⋀𝜒𝜑	Subs [𝜓↗𝜒] into ancom
7507	↔⋀𝜓𝜒⋀𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜒] into ancom
7508	→↔⋀𝜑𝜒⋀𝜒𝜑→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑	Subs [𝜑↗↔⋀𝜑𝜒⋀𝜒𝜑, 𝜓↗↔𝜑𝜓] into ax-1
7509	→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑	Modus ponens 7506, 7508
7510	↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜒𝜑] into pm5.74
7511	→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑] into biimp
7512	→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑	Modus ponens 7510, 7511
7513	↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑	Modus ponens 7509, 7512
7514	↔→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜒𝜑, 𝜒↗⋀𝜒𝜓] into pm5.74
7515	→↔→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓] into biimp
7516	→→↔𝜑𝜓↔⋀𝜒𝜑⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7514, 7515
7517	↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Modus ponens anbi2, 7516
7518	→↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp
7519	→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7517, 7518
7520	→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into biimp
7521	→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑	Modus ponens 7513, 7520
7522	→→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into ax-1
7523	→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7519, 7522
7524	→→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑, 𝜒↗→↔𝜑𝜓⋀𝜒𝜓] into ax-2
7525	→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7523, 7524
7526	→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7521, 7525
7527	→↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into bicom1
7528	↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑	Modus ponens 7517, 7527
7529	→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into biimp
7530	→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑	Modus ponens 7528, 7529
7531	→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜑↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑] into bicom1
7532	↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7513, 7531
7533	→↔→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜑, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into biimp
7534	→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7532, 7533
7535	→→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into ax-1
7536	→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7534, 7535
7537	→→→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜒𝜑→↔𝜑𝜓⋀𝜑𝜒→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜒𝜑, 𝜒↗→↔𝜑𝜓⋀𝜑𝜒] into ax-2
7538	→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜒𝜑→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7536, 7537
7539	→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7530, 7538
7540	→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into impbi
7541	→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7526, 7540
7542	↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7539, 7541
7543	↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜒𝜓] into pm5.74
7544	→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓] into bicom1
7545	↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓	Modus ponens 7543, 7544
7546	→↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓	Subs [𝜑↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓] into biimp
7547	→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓	Modus ponens 7545, 7546
7548	→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓	Modus ponens 7542, 7547
7549	→↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜒𝜓⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜒𝜓] into bicom1
7550	↔⋀𝜒𝜓⋀𝜓𝜒	Modus ponens 7507, 7549
7551	→↔⋀𝜒𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒	Subs [𝜑↗↔⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
7552	→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒	Modus ponens 7550, 7551
7553	→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓] into biimp
7554	→→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7543, 7553
7555	↔→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜓𝜒] into pm5.74
7556	→↔→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒, 𝜓↗↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒] into biimp
7557	→→↔𝜑𝜓↔⋀𝜒𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7555, 7556
7558	↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7552, 7557
7559	→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into biimp
7560	→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7558, 7559
7561	→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp
7562	→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into ax-1
7563	→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7560, 7562
7564	→→→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓, 𝜒↗→↔𝜑𝜓⋀𝜓𝜒] into ax-2
7565	→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7563, 7564
7566	→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7526, 7565
7567	→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into bicom1
7568	↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7558, 7567
7569	→↔→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into biimp
7570	→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓	Modus ponens 7568, 7569
7571	→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜒𝜓↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓] into bicom1
7572	↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7542, 7571
7573	→↔→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜒𝜓, 𝜓↗→↔𝜑𝜓⋀𝜑𝜒] into biimp
7574	→→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into ax-1
7575	→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7539, 7574
7576	→→→↔𝜑𝜓⋀𝜓𝜒→→↔𝜑𝜓⋀𝜒𝜓→↔𝜑𝜓⋀𝜑𝜒→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓⋀𝜒𝜓, 𝜒↗→↔𝜑𝜓⋀𝜑𝜒] into ax-2
7577	→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜒𝜓→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7575, 7576
7578	→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒	Modus ponens 7570, 7577
7579	→→→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓⋀𝜑𝜒, 𝜓↗→↔𝜑𝜓⋀𝜓𝜒] into impbi
7580	→→→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓⋀𝜑𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7566, 7579
7581	↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒	Modus ponens 7578, 7580
7582	↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜓𝜒] into pm5.74
7583	→↔→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒] into bicom1
7584	↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 7582, 7583
7585	→↔↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒, 𝜓↗→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒] into biimp
7586	→↔→↔𝜑𝜓⋀𝜑𝜒→↔𝜑𝜓⋀𝜓𝜒→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 7584, 7585
7587	→↔𝜑𝜓↔⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 7581, 7586	anbi1
7588	↔⋀𝜒𝜃⋀𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜃] into ancom
7589	→↔⋀𝜒𝜃⋀𝜃𝜒→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒	Subs [𝜑↗↔⋀𝜒𝜃⋀𝜃𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
7590	→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒	Modus ponens 7588, 7589
7591	↔→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗⋀𝜃𝜒] into pm5.32
7592	→↔→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒, 𝜓↗↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7593	→→⋀𝜑𝜓↔⋀𝜒𝜃⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7591, 7592
7594	↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7590, 7593
7595	→↔⋀𝜑𝜓⋀𝜓𝜑→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗⋀𝜃𝜒] into ax-1
7596	→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑	Modus ponens ancom, 7595
7597	↔→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜃𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.32
7598	→↔→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑	Subs [𝜑↗→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp
7599	→→⋀𝜃𝜒↔⋀𝜑𝜓⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑	Modus ponens 7597, 7598
7600	↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑	Modus ponens 7596, 7599
7601	↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜃𝜒] into ancom
7602	↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜓𝜑, 𝜓↗⋀𝜃𝜒] into ancom
7603	→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into bicom1
7604	↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7602, 7603
7605	→↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp
7606	→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7604, 7605
7607	→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp
7608	→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑	Modus ponens 7600, 7607
7609	→→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into ax-1
7610	→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7606, 7609
7611	→→⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2
7612	→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7610, 7611
7613	→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7608, 7612
7614	→↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1
7615	→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑	Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into biimp
7616	→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑	Modus ponens 7602, 7615
7617	→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜃𝜒⋀𝜓𝜑↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑] into bicom1
7618	↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓	Modus ponens 7600, 7617
7619	→↔⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp
7620	→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓	Modus ponens 7618, 7619
7621	→→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1
7622	→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓	Modus ponens 7620, 7621
7623	→→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜓𝜑⋀⋀𝜃𝜒⋀𝜑𝜓→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜃𝜒⋀𝜑𝜓] into ax-2
7624	→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Modus ponens 7622, 7623
7625	→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Modus ponens 7616, 7624
7626	→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi
7627	→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7613, 7626
7628	↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7625, 7627
7629	→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp
7630	→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp
7631	→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Modus ponens 7601, 7630
7632	→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into ax-1
7633	→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7613, 7632
7634	→→⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2
7635	→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7633, 7634
7636	→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7631, 7635
7637	→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1
7638	↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Modus ponens 7628, 7637
7639	→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into biimp
7640	→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓] into bicom1
7641	↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7601, 7640
7642	→↔⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7643	→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7641, 7642
7644	→→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1
7645	→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7643, 7644
7646	→→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜃𝜒⋀𝜑𝜓⋀⋀𝜑𝜓⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜃𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜑𝜓⋀𝜃𝜒] into ax-2
7647	→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜃𝜒⋀𝜑𝜓→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7645, 7646
7648	→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7625, 7647
7649	→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi
7650	→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7636, 7649
7651	↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7648, 7650
7652	→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into biimp
7653	→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7654	→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7594, 7653
7655	→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
7656	→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7636, 7655
7657	→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜒↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-2
7658	→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7656, 7657
7659	→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7654, 7658
7660	→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜓𝜑⋀𝜃𝜒↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into bicom1
7661	↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒	Modus ponens 7651, 7660
7662	→↔⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into biimp
7663	→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜃𝜒↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒] into bicom1
7664	↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7594, 7663
7665	→↔⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp
7666	→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7664, 7665
7667	→→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into ax-1
7668	→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7666, 7667
7669	→→⋀⋀𝜓𝜑⋀𝜃𝜒→⋀⋀𝜑𝜓⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜓𝜑⋀𝜃𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜃𝜒, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2
7670	→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜃𝜒→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7668, 7669
7671	→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7648, 7670
7672	→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜓𝜑⋀𝜃𝜒] into impbi
7673	→→⋀⋀𝜓𝜑⋀𝜃𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7659, 7672
7674	↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜓𝜑⋀𝜃𝜒	Modus ponens 7671, 7673	an2anr
7675	→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜃] into simpl
7676	→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃	Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜃] into simpr
7677	→↔𝜑𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜒] into ax-1
7678	→→↔𝜑𝜒→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7679	→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒	Modus ponens 7677, 7678
7680	→→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜑𝜒→𝜓↔𝜑𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗↔𝜑𝜒, 𝜒↗→𝜓↔𝜑𝜒] into ax-2
7681	→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒	Modus ponens 7679, 7680
7682	→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒	Modus ponens 7675, 7681
7683	↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑] into pm5.32
7684	→↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
7685	→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 7683, 7684
7686	→→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7687	→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 7685, 7686
7688	→→⋀↔𝜑𝜒↔𝜓𝜃→→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
7689	→→⋀↔𝜑𝜒↔𝜓𝜃→𝜓↔𝜑𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 7687, 7688
7690	→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 7682, 7689
7691	→↔⋀𝜑𝜓⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑	Subs [𝜑↗↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7692	→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑	Modus ponens ancom, 7691
7693	↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜑] into pm5.74
7694	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp
7695	→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Modus ponens 7693, 7694
7696	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Modus ponens 7692, 7695
7697	↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜓𝜒] into pm5.74
7698	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7699	→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜑⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7697, 7698
7700	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7690, 7699
7701	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7702	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7700, 7701
7703	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp
7704	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Modus ponens 7696, 7703
7705	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1
7706	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7702, 7705
7707	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into ax-2
7708	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7706, 7707
7709	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7704, 7708
7710	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1
7711	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Modus ponens 7700, 7710
7712	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into biimp
7713	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑	Modus ponens 7711, 7712
7714	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑] into bicom1
7715	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7696, 7714
7716	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp
7717	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7715, 7716
7718	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into ax-1
7719	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7717, 7718
7720	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2
7721	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜑→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7719, 7720
7722	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7713, 7721
7723	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into impbi
7724	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7709, 7723
7725	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7722, 7724
7726	↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜓𝜒] into pm5.74
7727	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1
7728	↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒	Modus ponens 7726, 7727
7729	→↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒	Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒] into biimp
7730	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒	Modus ponens 7728, 7729
7731	→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒	Modus ponens 7725, 7730
7732	→↔⋀𝜒𝜓⋀𝜓𝜒↔⋀𝜓𝜒⋀𝜒𝜓	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗⋀𝜓𝜒] into bicom1
7733	→↔⋀𝜓𝜒⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓	Subs [𝜑↗↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7734	→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓	Modus ponens 7507, 7733
7735	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7736	→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7726, 7735
7737	↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜒𝜓] into pm5.74
7738	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7739	→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜓𝜒⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7737, 7738
7740	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7734, 7739
7741	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7742	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7740, 7741
7743	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7744	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1
7745	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7742, 7744
7746	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into ax-2
7747	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7745, 7746
7748	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7709, 7747
7749	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1
7750	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7740, 7749
7751	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into biimp
7752	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒	Modus ponens 7750, 7751
7753	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒] into bicom1
7754	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7725, 7753
7755	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp
7756	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into ax-1
7757	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7722, 7756
7758	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2
7759	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜓𝜒→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7757, 7758
7760	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7752, 7759
7761	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into impbi
7762	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7748, 7761
7763	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7760, 7762
7764	↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜒𝜓] into pm5.74
7765	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1
7766	↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓	Modus ponens 7764, 7765
7767	→↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓	Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓] into biimp
7768	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓	Modus ponens 7766, 7767
7769	→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓	Modus ponens 7763, 7768
7770	→↔𝜓𝜃→𝜒↔𝜓𝜃	Subs [𝜑↗↔𝜓𝜃, 𝜓↗𝜒] into ax-1
7771	→→↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃	Subs [𝜑↗→↔𝜓𝜃→𝜒↔𝜓𝜃, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7772	→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃	Modus ponens 7770, 7771
7773	→→⋀↔𝜑𝜒↔𝜓𝜃→↔𝜓𝜃→𝜒↔𝜓𝜃→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗↔𝜓𝜃, 𝜒↗→𝜒↔𝜓𝜃] into ax-2
7774	→→⋀↔𝜑𝜒↔𝜓𝜃↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃	Modus ponens 7772, 7773
7775	→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃	Modus ponens 7676, 7774
7776	↔→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Subs [𝜑↗𝜒, 𝜒↗𝜃] into pm5.32
7777	→↔→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Subs [𝜑↗→𝜒↔𝜓𝜃, 𝜓↗↔⋀𝜒𝜓⋀𝜒𝜃] into biimp
7778	→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Modus ponens 7776, 7777
7779	→→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Subs [𝜑↗→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃, 𝜓↗⋀↔𝜑𝜒↔𝜓𝜃] into ax-1
7780	→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Modus ponens 7778, 7779
7781	→→⋀↔𝜑𝜒↔𝜓𝜃→→𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗→𝜒↔𝜓𝜃, 𝜒↗↔⋀𝜒𝜓⋀𝜒𝜃] into ax-2
7782	→→⋀↔𝜑𝜒↔𝜓𝜃→𝜒↔𝜓𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Modus ponens 7780, 7781
7783	→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃	Modus ponens 7775, 7782
7784	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7785	→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7764, 7784
7786	↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜒𝜓, 𝜒↗⋀𝜒𝜃] into pm5.74
7787	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into biimp
7788	→→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜒𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7786, 7787
7789	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7783, 7788
7790	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into biimp
7791	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7789, 7790
7792	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7793	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-1
7794	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7791, 7793
7795	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into ax-2
7796	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7794, 7795
7797	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7748, 7796
7798	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into bicom1
7799	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7789, 7798
7800	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into biimp
7801	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓	Modus ponens 7799, 7800
7802	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓] into bicom1
7803	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7763, 7802
7804	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into biimp
7805	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into ax-1
7806	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7760, 7805
7807	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓, 𝜒↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓] into ax-2
7808	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜓→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7806, 7807
7809	→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓	Modus ponens 7801, 7808
7810	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into impbi
7811	→→→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7797, 7810
7812	↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Modus ponens 7809, 7811
7813	↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃	Subs [𝜑↗⋀↔𝜑𝜒↔𝜓𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗⋀𝜒𝜃] into pm5.74
7814	→↔→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃] into bicom1
7815	↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7813, 7814
7816	→↔↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃, 𝜓↗→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃] into biimp
7817	→↔→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜑𝜓→⋀↔𝜑𝜒↔𝜓𝜃⋀𝜒𝜃→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7815, 7816
7818	→⋀↔𝜑𝜒↔𝜓𝜃↔⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 7812, 7817	pm4.38
7819	↔⋀𝜑𝜒⋀𝜑𝜒	Subs [𝜑↗⋀𝜑𝜒] into biid
7820	→↔⋀𝜑𝜒⋀𝜑𝜒→𝜓↔⋀𝜑𝜒⋀𝜑𝜒	Subs [𝜑↗↔⋀𝜑𝜒⋀𝜑𝜒] into ax-1
7821	→𝜓↔⋀𝜑𝜒⋀𝜑𝜒	Modus ponens 7819, 7820
7822	↔→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜒, 𝜒↗⋀𝜑𝜒] into pm5.32
7823	→↔→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗→𝜓↔⋀𝜑𝜒⋀𝜑𝜒, 𝜓↗↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒] into biimp
7824	→→𝜓↔⋀𝜑𝜒⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7822, 7823
7825	↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7821, 7824
7826	↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑] into anass
7827	→↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7828	↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7826, 7827
7829	→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
7830	→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7828, 7829
7831	→↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7832	→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7825, 7831
7833	→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1
7834	→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7830, 7833
7835	→→⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜓𝜑𝜒] into ax-2
7836	→→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7834, 7835
7837	→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into bicom1
7838	→↔⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7839	→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7826, 7838
7840	→↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7841	→→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into ax-1
7842	→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7832, 7841
7843	→→⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀𝜓⋀𝜑𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2
7844	→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7842, 7843
7845	→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into impbi
7846	→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7830, 7845
7847	→↔⋀𝜓𝜑⋀𝜑𝜓→𝜒↔⋀𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗𝜒] into ax-1
7848	→𝜒↔⋀𝜓𝜑⋀𝜑𝜓	Modus ponens 6162, 7847
7849	↔→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗⋀𝜓𝜑, 𝜒↗⋀𝜑𝜓] into pm5.32
7850	→↔→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓	Subs [𝜑↗→𝜒↔⋀𝜓𝜑⋀𝜑𝜓, 𝜓↗↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓] into biimp
7851	→→𝜒↔⋀𝜓𝜑⋀𝜑𝜓↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓	Modus ponens 7849, 7850
7852	↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓	Modus ponens 7848, 7851
7853	↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜓𝜑, 𝜓↗𝜒] into ancom
7854	↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ancom
7855	→↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓] into bicom1
7856	↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 7854, 7855
7857	→↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7858	→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 7856, 7857
7859	→↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓] into biimp
7860	→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓	Modus ponens 7852, 7859
7861	→→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into ax-1
7862	→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 7858, 7861
7863	→→⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒→→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7864	→→⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 7862, 7863
7865	→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 7860, 7864
7866	→↔⋀𝜒⋀𝜑𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7867	→↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓] into biimp
7868	→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓	Modus ponens 7854, 7867
7869	→↔⋀𝜒⋀𝜓𝜑⋀𝜒⋀𝜑𝜓↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜒⋀𝜑𝜓] into bicom1
7870	↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑	Modus ponens 7852, 7869
7871	→↔⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜒⋀𝜑𝜓, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
7872	→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑	Modus ponens 7870, 7871
7873	→→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑	Subs [𝜑↗→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7874	→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑	Modus ponens 7872, 7873
7875	→→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜑𝜓⋀𝜒⋀𝜓𝜑→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜑𝜓, 𝜒↗⋀𝜒⋀𝜓𝜑] into ax-2
7876	→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 7874, 7875
7877	→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 7868, 7876
7878	→→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi
7879	→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 7865, 7878
7880	↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 7877, 7879
7881	→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7882	→↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
7883	→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 7853, 7882
7884	→→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into ax-1
7885	→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 7865, 7884
7886	→→⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒→→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7887	→→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7885, 7886
7888	→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7883, 7887
7889	→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7890	↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 7880, 7889
7891	→↔⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
7892	→↔⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1
7893	↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒	Modus ponens 7853, 7892
7894	→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
7895	→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒	Modus ponens 7893, 7894
7896	→→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒	Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7897	→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒	Modus ponens 7895, 7896
7898	→→⋀⋀𝜑𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜓𝜑𝜒] into ax-2
7899	→→⋀⋀𝜑𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7897, 7898
7900	→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7877, 7899
7901	→→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi
7902	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7888, 7901
7903	↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7900, 7902
7904	→↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7905	→→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1
7906	→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7888, 7905
7907	→→⋀𝜓⋀𝜑𝜒→⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7908	→→⋀𝜓⋀𝜑𝜒⋀⋀𝜓𝜑𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7906, 7907
7909	→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7830, 7908
7910	→↔⋀⋀𝜓𝜑𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7911	↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7903, 7910
7912	→↔⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
7913	→→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7914	→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7839, 7913
7915	→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜓⋀𝜑𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2
7916	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7914, 7915
7917	→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7900, 7916
7918	→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into impbi
7919	→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7909, 7918
7920	↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7917, 7919
7921	→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
7922	↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7920, 7921	an21
7923	→↔⋀𝜓𝜒⋀𝜒𝜓→𝜑↔⋀𝜓𝜒⋀𝜒𝜓	Subs [𝜑↗↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗𝜑] into ax-1
7924	→𝜑↔⋀𝜓𝜒⋀𝜒𝜓	Modus ponens 7507, 7923
7925	↔→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓	Subs [𝜓↗⋀𝜓𝜒, 𝜒↗⋀𝜒𝜓] into pm5.32
7926	→↔→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑↔⋀𝜓𝜒⋀𝜒𝜓, 𝜓↗↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓] into biimp
7927	→→𝜑↔⋀𝜓𝜒⋀𝜒𝜓↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓	Modus ponens 7925, 7926
7928	↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓	Modus ponens 7924, 7927
7929	↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓	Subs [𝜓↗𝜒, 𝜒↗𝜓] into anass
7930	→↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓] into bicom1
7931	↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓	Modus ponens 7929, 7930
7932	→↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp
7933	→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓	Modus ponens 7931, 7932
7934	→↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓] into biimp
7935	→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓	Modus ponens 7928, 7934
7936	→→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓	Subs [𝜑↗→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
7937	→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓	Modus ponens 7933, 7936
7938	→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓, 𝜒↗⋀⋀𝜑𝜒𝜓] into ax-2
7939	→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7937, 7938
7940	→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7935, 7939
7941	→↔⋀𝜑⋀𝜒𝜓⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1
7942	→↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓] into biimp
7943	→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓	Modus ponens 7929, 7942
7944	→↔⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜒𝜓↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜒𝜓] into bicom1
7945	↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 7928, 7944
7946	→↔⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
7947	→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 7945, 7946
7948	→→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into ax-1
7949	→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 7947, 7948
7950	→→⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜒𝜓⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜒𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
7951	→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜒𝜓→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 7949, 7950
7952	→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 7943, 7951
7953	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into impbi
7954	→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7940, 7953
7955	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7952, 7954
7956	↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜒] into ancom
7957	→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1
7958	↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒	Modus ponens 7956, 7957
7959	→↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7960	→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒	Modus ponens 7958, 7959
7961	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp
7962	→→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒	Subs [𝜑↗→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
7963	→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒	Modus ponens 7960, 7962
7964	→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓, 𝜒↗⋀𝜓⋀𝜑𝜒] into ax-2
7965	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7963, 7964
7966	→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7940, 7965
7967	→↔⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7968	→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into biimp
7969	→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7956, 7968
7970	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜒𝜓↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into bicom1
7971	↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 7955, 7970
7972	→↔⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
7973	→→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into ax-1
7974	→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒	Modus ponens 7952, 7973
7975	→→⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀𝜑⋀𝜓𝜒→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
7976	→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 7974, 7975
7977	→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 7969, 7976
7978	→→⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒→→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into impbi
7979	→→⋀𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7966, 7978
7980	↔⋀𝜑⋀𝜓𝜒⋀𝜓⋀𝜑𝜒	Modus ponens 7977, 7979	an12
7981	→↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into biimp
7982	→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
7983	→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7969, 7982
7984	→→⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜑𝜒𝜓] into ax-2
7985	→→⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7983, 7984
7986	→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7917, 7985
7987	→↔⋀⋀𝜑𝜓𝜒⋀𝜓⋀𝜑𝜒↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜓⋀𝜑𝜒] into bicom1
7988	→↔⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
7989	→→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into ax-1
7990	→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 7909, 7989
7991	→→⋀⋀𝜑𝜒𝜓→⋀𝜓⋀𝜑𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜒𝜓, 𝜓↗⋀𝜓⋀𝜑𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
7992	→→⋀⋀𝜑𝜒𝜓⋀𝜓⋀𝜑𝜒→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 7990, 7991
7993	→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒	Modus ponens 7960, 7992
7994	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓→→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒𝜓] into impbi
7995	→→⋀⋀𝜑𝜒𝜓⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7986, 7994
7996	↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒𝜓	Modus ponens 7993, 7995	an32
7997	↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜑] into an21
7998	→↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
7999	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7997, 7998
8000	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into biimp
8001	→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒	Modus ponens 7999, 8000
8002	→→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8003	→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 7883, 8002
8004	→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜒⋀𝜓𝜑→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜒⋀𝜓𝜑] into ax-2
8005	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 8003, 8004
8006	→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 8001, 8005
8007	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜑𝜒↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜑𝜒] into bicom1
8008	→↔⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8009	→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 7997, 8008
8010	→→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into ax-1
8011	→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8009, 8010
8012	→→⋀𝜒⋀𝜓𝜑→⋀⋀𝜓𝜑𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜓𝜑𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8013	→→⋀𝜒⋀𝜓𝜑⋀⋀𝜓𝜑𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8011, 8012
8014	→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 7895, 8013
8015	→→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into impbi
8016	→→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 8006, 8015
8017	↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑	Modus ponens 8014, 8016	an13
8018	↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑	Subs [𝜑↗𝜒, 𝜒↗𝜑] into anass
8019	→↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑	Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1
8020	↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑	Modus ponens 8018, 8019
8021	→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜒𝜓𝜑] into biimp
8022	→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑	Modus ponens 8020, 8021
8023	→↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
8024	→→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑	Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8025	→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑	Modus ponens 8022, 8024
8026	→→⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑→→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀⋀𝜒𝜓𝜑] into ax-2
8027	→→⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8025, 8026
8028	→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8006, 8027
8029	→↔⋀𝜒⋀𝜓𝜑⋀⋀𝜒𝜓𝜑↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀⋀𝜒𝜓𝜑] into bicom1
8030	→↔⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑	Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑] into biimp
8031	→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑	Modus ponens 8018, 8030
8032	→↔⋀𝜑⋀𝜓𝜒⋀𝜒⋀𝜓𝜑↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒⋀𝜓𝜑] into bicom1
8033	↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Modus ponens an13, 8032
8034	→↔⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜒⋀𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8035	→→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into ax-1
8036	→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8014, 8035
8037	→→⋀⋀𝜒𝜓𝜑→⋀𝜒⋀𝜓𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜒⋀𝜓𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8038	→→⋀⋀𝜒𝜓𝜑⋀𝜒⋀𝜓𝜑→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8036, 8037
8039	→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8031, 8038
8040	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into impbi
8041	→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8028, 8040
8042	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8039, 8041
8043	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into biimp
8044	→↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8045	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8046	→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8028, 8045
8047	→→⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜒𝜓𝜑] into ax-2
8048	→→⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8046, 8047
8049	→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 5253, 8048
8050	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜒𝜓𝜑↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into bicom1
8051	↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8042, 8050
8052	→↔⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8053	→↔⋀⋀𝜑𝜓𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8054	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens anass, 8053
8055	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
8056	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into ax-1
8057	→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 5573, 8056
8058	→→⋀⋀𝜒𝜓𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜒𝜓𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
8059	→→⋀⋀𝜒𝜓𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 8057, 8058
8060	→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒	Modus ponens 8039, 8059
8061	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑→→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜒𝜓𝜑] into impbi
8062	→→⋀⋀𝜒𝜓𝜑⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8049, 8061
8063	↔⋀⋀𝜑𝜓𝜒⋀⋀𝜒𝜓𝜑	Modus ponens 8060, 8062	an31
8064	↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜒↗⋀𝜒𝜃] into anass
8065	↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜃] into an12
8066	→↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃	Subs [𝜑↗↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃, 𝜓↗𝜑] into ax-1
8067	→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃	Modus ponens 8065, 8066
8068	↔→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Subs [𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗⋀𝜒⋀𝜓𝜃] into pm5.32
8069	→↔→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃, 𝜓↗↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp
8070	→→𝜑↔⋀𝜓⋀𝜒𝜃⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Modus ponens 8068, 8069
8071	↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Modus ponens 8067, 8070
8072	↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Subs [𝜓↗𝜒, 𝜒↗⋀𝜓𝜃] into anass
8073	→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into bicom1
8074	↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8072, 8073
8075	→↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8076	→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8074, 8075
8077	→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp
8078	→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Modus ponens 8071, 8077
8079	→→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1
8080	→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8076, 8079
8081	→→⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-2
8082	→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8080, 8081
8083	→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8078, 8082
8084	→↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1
8085	→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into biimp
8086	→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃	Modus ponens 8072, 8085
8087	→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀𝜑⋀𝜒⋀𝜓𝜃↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃] into bicom1
8088	↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 8071, 8087
8089	→↔⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp
8090	→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 8088, 8089
8091	→→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-1
8092	→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 8090, 8091
8093	→→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜒⋀𝜓𝜃, 𝜒↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-2
8094	→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 8092, 8093
8095	→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 8086, 8094
8096	→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into impbi
8097	→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8083, 8096
8098	↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8095, 8097
8099	→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8100	→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp
8101	→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 8064, 8100
8102	→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
8103	→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8083, 8102
8104	→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-2
8105	→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8103, 8104
8106	→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8101, 8105
8107	→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1
8108	↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 8098, 8107
8109	→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into biimp
8110	→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑⋀𝜓⋀𝜒𝜃↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into bicom1
8111	↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8064, 8110
8112	→↔⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp
8113	→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8111, 8112
8114	→→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into ax-1
8115	→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8113, 8114
8116	→→⋀⋀𝜑𝜒⋀𝜓𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2
8117	→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀𝜑⋀𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8115, 8116
8118	→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8095, 8117
8119	→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into impbi
8120	→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8106, 8119
8121	↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8118, 8120	an4
8122	↔⋀𝜓𝜃⋀𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜃] into ancom
8123	→↔⋀𝜓𝜃⋀𝜃𝜓→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓	Subs [𝜑↗↔⋀𝜓𝜃⋀𝜃𝜓, 𝜓↗⋀𝜑𝜒] into ax-1
8124	→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓	Modus ponens 8122, 8123
8125	↔→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗⋀𝜓𝜃, 𝜒↗⋀𝜃𝜓] into pm5.32
8126	→↔→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Subs [𝜑↗→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓, 𝜓↗↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓] into biimp
8127	→→⋀𝜑𝜒↔⋀𝜓𝜃⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8125, 8126
8128	↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8124, 8127
8129	→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into biimp
8130	→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8128, 8129
8131	→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8132	→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Subs [𝜑↗→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
8133	→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8130, 8132
8134	→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜒⋀𝜃𝜓] into ax-2
8135	→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8133, 8134
8136	→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8106, 8135
8137	→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜒⋀𝜃𝜓↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into bicom1
8138	↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8128, 8137
8139	→↔⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into biimp
8140	→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 8138, 8139
8141	→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜓𝜃↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃] into bicom1
8142	↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens an4, 8141
8143	→↔⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into biimp
8144	→→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into ax-1
8145	→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8118, 8144
8146	→→⋀⋀𝜑𝜒⋀𝜃𝜓→⋀⋀𝜑𝜒⋀𝜓𝜃⋀⋀𝜑𝜓⋀𝜒𝜃→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜃𝜓, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-2
8147	→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜒⋀𝜓𝜃→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8145, 8146
8148	→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃	Modus ponens 8140, 8147
8149	→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜒⋀𝜃𝜓] into impbi
8150	→→⋀⋀𝜑𝜒⋀𝜃𝜓⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8136, 8149
8151	↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜒⋀𝜃𝜓	Modus ponens 8148, 8150	an42
8152	↔⋀⋀𝜑𝜃⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜃	Subs [𝜓↗𝜃, 𝜒↗𝜓, 𝜃↗𝜒] into an42
8153	→↔⋀⋀𝜑𝜃⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜃↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜃⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into bicom1
8154	↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒	Modus ponens 8152, 8153	an43
8155	→↔⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜃⋀𝜓𝜒] into biimp
8156	→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒	Modus ponens an43, 8155
8157	→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃	Subs [𝜑↗⋀𝜑𝜃, 𝜓↗⋀𝜓𝜒] into simpl
8158	→→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃	Subs [𝜑↗→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜃] into ax-1
8159	→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃	Modus ponens 8157, 8158
8160	→→⋀⋀𝜑𝜓⋀𝜒𝜃→⋀⋀𝜑𝜃⋀𝜓𝜒⋀𝜑𝜃→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜃, 𝜓↗⋀⋀𝜑𝜃⋀𝜓𝜒, 𝜒↗⋀𝜑𝜃] into ax-2
8161	→→⋀⋀𝜑𝜓⋀𝜒𝜃⋀⋀𝜑𝜃⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃	Modus ponens 8159, 8160
8162	→⋀⋀𝜑𝜓⋀𝜒𝜃⋀𝜑𝜃	Modus ponens 8156, 8161	an3
8163	↔→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑] into pm4.71
8164	→↔→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑→→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑	Subs [𝜑↗→⋀𝜑𝜓𝜑, 𝜓↗↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑] into biimp
8165	→→⋀𝜑𝜓𝜑↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑	Modus ponens 8163, 8164
8166	↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑	Modus ponens simpl, 8165
8167	→↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜑↔⋀⋀𝜑𝜓𝜑⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜑] into bicom1
8168	↔⋀⋀𝜑𝜓𝜑⋀𝜑𝜓	Modus ponens 8166, 8167	anabs1
8169	↔↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into bicom
8170	→↔↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓	Subs [𝜑↗↔𝜓⋀𝜑𝜓, 𝜓↗↔⋀𝜑𝜓𝜓] into biimp
8171	→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓	Modus ponens 8169, 8170
8172	→→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓	Subs [𝜑↗→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
8173	→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓	Modus ponens 8171, 8172
8174	→→𝜑→↔𝜓⋀𝜑𝜓↔⋀𝜑𝜓𝜓→→𝜑↔𝜓⋀𝜑𝜓→𝜑↔⋀𝜑𝜓𝜓	Subs [𝜓↗↔𝜓⋀𝜑𝜓, 𝜒↗↔⋀𝜑𝜓𝜓] into ax-2
8175	→→𝜑↔𝜓⋀𝜑𝜓→𝜑↔⋀𝜑𝜓𝜓	Modus ponens 8173, 8174
8176	→𝜑↔⋀𝜑𝜓𝜓	Modus ponens ibar, 8175
8177	↔→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into pm5.32
8178	→↔→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓→→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗→𝜑↔⋀𝜑𝜓𝜓, 𝜓↗↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓] into biimp
8179	→→𝜑↔⋀𝜑𝜓𝜓↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 8177, 8178
8180	↔⋀𝜑⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 8176, 8179	anabs5
8181	↔→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜓] into pm4.71
8182	→↔→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓] into biimp
8183	→→⋀𝜑𝜓𝜓↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Modus ponens 8181, 8182
8184	↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Modus ponens simpr, 8183
8185	↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into ancom
8186	→↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into bicom1
8187	↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓	Modus ponens 8185, 8186
8188	→↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into biimp
8189	→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓	Modus ponens 8187, 8188
8190	→↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into biimp
8191	→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Modus ponens 8184, 8190
8192	→→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓	Subs [𝜑↗→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8193	→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓	Modus ponens 8189, 8192
8194	→→⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓→→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓, 𝜒↗⋀𝜓⋀𝜑𝜓] into ax-2
8195	→→⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓	Modus ponens 8193, 8194
8196	→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓	Modus ponens 8191, 8195
8197	→↔⋀⋀𝜑𝜓𝜓⋀𝜓⋀𝜑𝜓↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into bicom1
8198	→↔⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into biimp
8199	→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓	Modus ponens 8185, 8198
8200	→↔⋀𝜑𝜓⋀⋀𝜑𝜓𝜓↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓] into bicom1
8201	↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓	Modus ponens 8184, 8200
8202	→↔⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜓, 𝜓↗⋀𝜑𝜓] into biimp
8203	→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓	Modus ponens 8201, 8202
8204	→→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓	Subs [𝜑↗→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into ax-1
8205	→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓	Modus ponens 8203, 8204
8206	→→⋀𝜓⋀𝜑𝜓→⋀⋀𝜑𝜓𝜓⋀𝜑𝜓→→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜓⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜓, 𝜒↗⋀𝜑𝜓] into ax-2
8207	→→⋀𝜓⋀𝜑𝜓⋀⋀𝜑𝜓𝜓→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 8205, 8206
8208	→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 8199, 8207
8209	→→⋀𝜑𝜓⋀𝜓⋀𝜑𝜓→→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into impbi
8210	→→⋀𝜓⋀𝜑𝜓⋀𝜑𝜓↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓	Modus ponens 8196, 8209
8211	↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓	Modus ponens 8208, 8210
8212	→↔⋀𝜑𝜓⋀𝜓⋀𝜑𝜓↔⋀𝜓⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜓⋀𝜑𝜓] into bicom1
8213	↔⋀𝜓⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 8211, 8212	anabs7
8214	→↔⋀𝜑𝜑𝜑→⋀𝜓𝜒↔⋀𝜑𝜑𝜑	Subs [𝜑↗↔⋀𝜑𝜑𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
8215	→⋀𝜓𝜒↔⋀𝜑𝜑𝜑	Modus ponens anidm, 8214
8216	↔→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜑𝜑, 𝜒↗𝜑] into pm5.32
8217	→↔→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑	Subs [𝜑↗→⋀𝜓𝜒↔⋀𝜑𝜑𝜑, 𝜓↗↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑] into biimp
8218	→→⋀𝜓𝜒↔⋀𝜑𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑	Modus ponens 8216, 8217
8219	↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑	Modus ponens 8215, 8218
8220	↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗⋀𝜑𝜑, 𝜓↗⋀𝜓𝜒] into ancom
8221	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑	Subs [𝜓↗⋀𝜓𝜒] into ancom
8222	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into bicom1
8223	↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8221, 8222
8224	→↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8225	→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8223, 8224
8226	→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑	Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp
8227	→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑	Modus ponens 8219, 8226
8228	→→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into ax-1
8229	→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8225, 8228
8230	→→⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8231	→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8229, 8230
8232	→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8227, 8231
8233	→↔⋀⋀𝜓𝜒𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8234	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp
8235	→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑	Modus ponens 8221, 8234
8236	→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜓𝜒𝜑↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into bicom1
8237	↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑	Modus ponens 8219, 8236
8238	→↔⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp
8239	→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑	Modus ponens 8237, 8238
8240	→→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8241	→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑	Modus ponens 8239, 8240
8242	→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜑⋀⋀𝜓𝜒⋀𝜑𝜑→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗⋀⋀𝜓𝜒⋀𝜑𝜑] into ax-2
8243	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Modus ponens 8241, 8242
8244	→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Modus ponens 8235, 8243
8245	→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi
8246	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8232, 8245
8247	↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8244, 8246
8248	→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8249	→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp
8250	→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Modus ponens 8220, 8249
8251	→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into ax-1
8252	→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒	Modus ponens 8232, 8251
8253	→→⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8254	→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8252, 8253
8255	→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8250, 8254
8256	→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8257	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Modus ponens 8247, 8256
8258	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into biimp
8259	→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑] into bicom1
8260	↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8220, 8259
8261	→↔⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp
8262	→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8260, 8261
8263	→→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8264	→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8262, 8263
8265	→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒⋀𝜑𝜑⋀⋀𝜑𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒⋀𝜑𝜑, 𝜒↗⋀⋀𝜑𝜑⋀𝜓𝜒] into ax-2
8266	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜓𝜒⋀𝜑𝜑→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8264, 8265
8267	→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8244, 8266
8268	→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into impbi
8269	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8255, 8268
8270	↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8267, 8269
8271	↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜓↗𝜑, 𝜒↗𝜓, 𝜃↗𝜒] into an4
8272	→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into bicom1
8273	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8270, 8272
8274	→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into biimp
8275	→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 8271, 8274
8276	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp
8277	→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
8278	→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 8275, 8277
8279	→→⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜒↗⋀⋀𝜑𝜓⋀𝜑𝜒] into ax-2
8280	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 8278, 8279
8281	→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 8267, 8280
8282	→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into bicom1
8283	↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8271, 8282
8284	→↔⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into biimp
8285	→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒	Modus ponens 8283, 8284
8286	→↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜑⋀𝜓𝜒↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒] into bicom1
8287	→↔⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into biimp
8288	→→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into ax-1
8289	→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8255, 8288
8290	→→⋀⋀𝜑𝜓⋀𝜑𝜒→⋀⋀𝜑𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜑𝜒, 𝜓↗⋀⋀𝜑𝜑⋀𝜓𝜒, 𝜒↗⋀𝜑⋀𝜓𝜒] into ax-2
8291	→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀⋀𝜑𝜑⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8289, 8290
8292	→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒	Modus ponens 8285, 8291
8293	→→⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜑𝜒] into impbi
8294	→→⋀⋀𝜑𝜓⋀𝜑𝜒⋀𝜑⋀𝜓𝜒↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 8281, 8293
8295	↔⋀𝜑⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜑𝜒	Modus ponens 8292, 8294	anandi
8296	↔⋀𝜒𝜒𝜒	Subs [𝜑↗𝜒] into anidm
8297	→↔⋀𝜒𝜒𝜒→⋀𝜑𝜓↔⋀𝜒𝜒𝜒	Subs [𝜑↗↔⋀𝜒𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
8298	→⋀𝜑𝜓↔⋀𝜒𝜒𝜒	Modus ponens 8296, 8297
8299	↔→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜒𝜒] into pm5.32
8300	→↔→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓↔⋀𝜒𝜒𝜒, 𝜓↗↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒] into biimp
8301	→→⋀𝜑𝜓↔⋀𝜒𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 8299, 8300
8302	↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 8298, 8301
8303	↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜃↗𝜒] into an4
8304	→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into bicom1
8305	↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Modus ponens 8302, 8304
8306	→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into biimp
8307	→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 8303, 8306
8308	→↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into biimp
8309	→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Modus ponens 8305, 8308
8310	→→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8311	→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 8307, 8310
8312	→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜒↗⋀⋀𝜑𝜒⋀𝜓𝜒] into ax-2
8313	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 8311, 8312
8314	→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 8309, 8313
8315	→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜒⋀𝜓𝜒↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into bicom1
8316	↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Modus ponens 8303, 8315
8317	→↔⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into biimp
8318	→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒	Modus ponens 8316, 8317
8319	→↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒] into bicom1
8320	→↔⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into biimp
8321	→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 8302, 8320
8322	→→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into ax-1
8323	→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 8321, 8322
8324	→→⋀⋀𝜑𝜒⋀𝜓𝜒→⋀⋀𝜑𝜓⋀𝜒𝜒⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜒⋀𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓⋀𝜒𝜒, 𝜒↗⋀⋀𝜑𝜓𝜒] into ax-2
8325	→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓⋀𝜒𝜒→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 8323, 8324
8326	→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒	Modus ponens 8318, 8325
8327	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜒⋀𝜓𝜒] into impbi
8328	→→⋀⋀𝜑𝜒⋀𝜓𝜒⋀⋀𝜑𝜓𝜒↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 8314, 8327
8329	↔⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜒⋀𝜓𝜒	Modus ponens 8326, 8328	anandir
8330	↔⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒] into df-an
8331	→¬¬→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→𝜓𝜒] into notnotr
8332	→→𝜓𝜒→→𝜑𝜓→𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
8333	→→→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→→𝜑𝜓→𝜓𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1
8334	→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒	Modus ponens 8332, 8333
8335	→→¬¬→𝜓𝜒→→𝜓𝜒→→𝜑𝜓→𝜓𝜒→→¬¬→𝜓𝜒→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒	Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜓𝜒] into ax-2
8336	→→¬¬→𝜓𝜒→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒	Modus ponens 8334, 8335
8337	→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒	Modus ponens 8331, 8336
8338	→→→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
8339	→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens imim1, 8338
8340	→→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1
8341	→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 8339, 8340
8342	→→¬¬→𝜓𝜒→→→𝜑𝜓→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→→𝜑𝜓→𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
8343	→→¬¬→𝜓𝜒→→𝜑𝜓→𝜓𝜒→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 8341, 8342
8344	→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 8337, 8343
8345	→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜓𝜒] into ax-1
8346	→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
8347	→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓	Modus ponens 8345, 8346
8348	→→→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜓𝜒→𝜑𝜓] into ax-2
8349	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓	Modus ponens 8347, 8348
8350	→→¬¬→𝜓𝜒→→𝜑𝜓→𝜑𝜒→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒	Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
8351	→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒	Modus ponens 8344, 8350
8352	→→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
8353	→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒	Modus ponens 8351, 8352
8354	→→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒→𝜑𝜓, 𝜒↗→¬¬→𝜓𝜒→𝜑𝜒] into ax-2
8355	→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜓→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒	Modus ponens 8353, 8354
8356	→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒	Modus ponens 8345, 8355
8357	→→𝜑𝜒¬¬→𝜑𝜒	Subs [𝜑↗→𝜑𝜒] into notnot
8358	→→→𝜑𝜒¬¬→𝜑𝜒→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒¬¬→𝜑𝜒, 𝜓↗¬¬→𝜓𝜒] into ax-1
8359	→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒	Modus ponens 8357, 8358
8360	→→¬¬→𝜓𝜒→→𝜑𝜒¬¬→𝜑𝜒→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒	Subs [𝜑↗¬¬→𝜓𝜒, 𝜓↗→𝜑𝜒, 𝜒↗¬¬→𝜑𝜒] into ax-2
8361	→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒	Modus ponens 8359, 8360
8362	→→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒	Subs [𝜑↗→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
8363	→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒	Modus ponens 8361, 8362
8364	→→→𝜑𝜓→→¬¬→𝜓𝜒→𝜑𝜒→¬¬→𝜓𝜒¬¬→𝜑𝜒→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒→𝜑𝜒, 𝜒↗→¬¬→𝜓𝜒¬¬→𝜑𝜒] into ax-2
8365	→→→𝜑𝜓→¬¬→𝜓𝜒→𝜑𝜒→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒	Modus ponens 8363, 8364
8366	→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒	Modus ponens 8356, 8365
8367	→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒	Subs [𝜑↗¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-3
8368	→→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒	Subs [𝜑↗→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
8369	→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒	Modus ponens 8367, 8368
8370	→→→𝜑𝜓→→¬¬→𝜓𝜒¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜓𝜒→→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜓𝜒¬¬→𝜑𝜒, 𝜒↗→¬→𝜑𝜒¬→𝜓𝜒] into ax-2
8371	→→→𝜑𝜓→¬¬→𝜓𝜒¬¬→𝜑𝜒→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒	Modus ponens 8369, 8370
8372	→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒	Modus ponens 8366, 8371
8373	→¬→𝜑𝜒¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒] into id
8374	→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→𝜑𝜓] into ax-1
8375	→→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8376	→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒	Modus ponens 8374, 8375
8377	→→¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→→𝜑𝜓¬→𝜑𝜒] into ax-2
8378	→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒	Modus ponens 8376, 8377
8379	→→→𝜑𝜓→¬→𝜑𝜒¬→𝜓𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→𝜓𝜒] into ax-2
8380	→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8372, 8379
8381	→→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8382	→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8380, 8381
8383	→→¬→𝜑𝜒→→→𝜑𝜓¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜑𝜒, 𝜒↗→→𝜑𝜓¬→𝜓𝜒] into ax-2
8384	→→¬→𝜑𝜒→→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8382, 8383
8385	→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8374, 8384
8386	→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒] into id
8387	→→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8388	→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8386, 8387
8389	→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒] into notnotr
8390	→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8391	→→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1
8392	→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8390, 8391
8393	→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8394	→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8392, 8393
8395	→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8389, 8394
8396	→→¬→𝜑𝜒→¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8397	→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8388, 8396
8398	→→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1
8399	→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8397, 8398
8400	→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8401	→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8399, 8400
8402	→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-1
8403	→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8404	→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒	Modus ponens 8402, 8403
8405	→→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒] into ax-2
8406	→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒	Modus ponens 8404, 8405
8407	→→¬¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8408	→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8395, 8407
8409	→→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8410	→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8408, 8409
8411	→→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8412	→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8410, 8411
8413	→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8402, 8412
8414	→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗→→𝜑𝜓¬→𝜓𝜒] into ax-3
8415	→→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8416	→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8414, 8415
8417	→→¬→𝜑𝜒→→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8418	→→¬→𝜑𝜒→¬¬¬→→𝜑𝜓¬→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8416, 8417
8419	→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8413, 8418
8420	→→¬→𝜑𝜒→→→𝜑𝜓¬→𝜓𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→𝜓𝜒, 𝜒↗¬¬→→𝜑𝜓¬→𝜓𝜒] into ax-2
8421	→→¬→𝜑𝜒→→𝜑𝜓¬→𝜓𝜒→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8419, 8420
8422	→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8385, 8421
8423	→→¬→𝜑𝜒¬¬→→𝜑𝜓¬→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒] into ax-3
8424	→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒	Modus ponens 8422, 8423
8425	→↔⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒] into biimp
8426	→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒	Modus ponens 8330, 8425
8427	→→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒, 𝜓↗⋀→𝜑𝜓→𝜓𝜒] into ax-1
8428	→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒	Modus ponens 8424, 8427
8429	→→⋀→𝜑𝜓→𝜓𝜒→¬→→𝜑𝜓¬→𝜓𝜒→𝜑𝜒→→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒	Subs [𝜑↗⋀→𝜑𝜓→𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
8430	→→⋀→𝜑𝜓→𝜓𝜒¬→→𝜑𝜓¬→𝜓𝜒→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒	Modus ponens 8428, 8429
8431	→⋀→𝜑𝜓→𝜓𝜒→𝜑𝜒	Modus ponens 8426, 8430	pm3.33
8432	↔⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜑𝜓] into df-an
8433	→→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜓𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
8434	→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 63, 8433
8435	→→¬¬→𝜑𝜓→→𝜑𝜓→→𝜓𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜓] into ax-2
8436	→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 8434, 8435
8437	→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓	Modus ponens 532, 8436
8438	→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 68, 78
8439	→→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
8440	→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 8438, 8439
8441	→→¬¬→𝜑𝜓→→→𝜓𝜒→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→→𝜓𝜒→𝜑𝜓, 𝜒↗→→𝜓𝜒→𝜑𝜒] into ax-2
8442	→→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 8440, 8441
8443	→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒	Modus ponens 8437, 8442
8444	→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
8445	→→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
8446	→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒	Modus ponens 8444, 8445
8447	→→→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜓𝜒] into ax-2
8448	→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒	Modus ponens 8446, 8447
8449	→→¬¬→𝜑𝜓→→𝜓𝜒→𝜑𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
8450	→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒	Modus ponens 8443, 8449
8451	→→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
8452	→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒	Modus ponens 8450, 8451
8453	→→→𝜓𝜒→→¬¬→𝜑𝜓→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑𝜒] into ax-2
8454	→→→𝜓𝜒→¬¬→𝜑𝜓→𝜓𝜒→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒	Modus ponens 8452, 8453
8455	→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒	Modus ponens 8444, 8454
8456	→→→𝜑𝜒¬¬→𝜑𝜒→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒¬¬→𝜑𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
8457	→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒	Modus ponens 8357, 8456
8458	→→¬¬→𝜑𝜓→→𝜑𝜒¬¬→𝜑𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗¬¬→𝜑𝜒] into ax-2
8459	→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒	Modus ponens 8457, 8458
8460	→→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒	Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
8461	→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒	Modus ponens 8459, 8460
8462	→→→𝜓𝜒→→¬¬→𝜑𝜓→𝜑𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑𝜒, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑𝜒] into ax-2
8463	→→→𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜒→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒	Modus ponens 8461, 8462
8464	→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒	Modus ponens 8455, 8463
8465	→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-3
8466	→→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓, 𝜓↗→𝜓𝜒] into ax-1
8467	→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓	Modus ponens 8465, 8466
8468	→→→𝜓𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜒→¬→𝜑𝜒¬→𝜑𝜓→→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓	Subs [𝜑↗→𝜓𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑𝜒, 𝜒↗→¬→𝜑𝜒¬→𝜑𝜓] into ax-2
8469	→→→𝜓𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜒→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓	Modus ponens 8467, 8468
8470	→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓	Modus ponens 8464, 8469
8471	→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→𝜓𝜒] into ax-1
8472	→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8473	→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒	Modus ponens 8471, 8472
8474	→→¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→→𝜓𝜒¬→𝜑𝜒] into ax-2
8475	→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒	Modus ponens 8473, 8474
8476	→→→𝜓𝜒→¬→𝜑𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→𝜓𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→𝜑𝜓] into ax-2
8477	→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8470, 8476
8478	→→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8479	→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8477, 8478
8480	→→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜓𝜒¬→𝜑𝜒, 𝜒↗→→𝜓𝜒¬→𝜑𝜓] into ax-2
8481	→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜒→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8479, 8480
8482	→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8471, 8481
8483	→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓] into id
8484	→→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8485	→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8483, 8484
8486	→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓] into notnotr
8487	→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8488	→→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1
8489	→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8487, 8488
8490	→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8491	→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8489, 8490
8492	→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8486, 8491
8493	→→¬→𝜑𝜒→¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8494	→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8485, 8493
8495	→→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1
8496	→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8494, 8495
8497	→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8498	→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8496, 8497
8499	→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-1
8500	→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒] into ax-1
8501	→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒	Modus ponens 8499, 8500
8502	→→¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒] into ax-2
8503	→→¬→𝜑𝜒¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒	Modus ponens 8501, 8502
8504	→→¬¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬→→𝜓𝜒¬→𝜑𝜓→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒, 𝜒↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8505	→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8492, 8504
8506	→→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8507	→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8505, 8506
8508	→→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒, 𝜒↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8509	→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→𝜑𝜒→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8507, 8508
8510	→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8499, 8509
8511	→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗→→𝜓𝜒¬→𝜑𝜓] into ax-3
8512	→→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜒] into ax-1
8513	→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8511, 8512
8514	→→¬→𝜑𝜒→→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8515	→→¬→𝜑𝜒→¬¬¬→→𝜓𝜒¬→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8513, 8514
8516	→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8510, 8515
8517	→→¬→𝜑𝜒→→→𝜓𝜒¬→𝜑𝜓¬¬→→𝜓𝜒¬→𝜑𝜓→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜒, 𝜓↗→→𝜓𝜒¬→𝜑𝜓, 𝜒↗¬¬→→𝜓𝜒¬→𝜑𝜓] into ax-2
8518	→→¬→𝜑𝜒→→𝜓𝜒¬→𝜑𝜓→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8516, 8517
8519	→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8482, 8518
8520	→→¬→𝜑𝜒¬¬→→𝜓𝜒¬→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜒, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓] into ax-3
8521	→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒	Modus ponens 8519, 8520
8522	→↔⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Subs [𝜑↗⋀→𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓] into biimp
8523	→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓	Modus ponens 8432, 8522
8524	→→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒, 𝜓↗⋀→𝜓𝜒→𝜑𝜓] into ax-1
8525	→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒	Modus ponens 8521, 8524
8526	→→⋀→𝜓𝜒→𝜑𝜓→¬→→𝜓𝜒¬→𝜑𝜓→𝜑𝜒→→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒	Subs [𝜑↗⋀→𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜓𝜒¬→𝜑𝜓, 𝜒↗→𝜑𝜒] into ax-2
8527	→→⋀→𝜓𝜒→𝜑𝜓¬→→𝜓𝜒¬→𝜑𝜓→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 8525, 8526
8528	→⋀→𝜓𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 8523, 8527	pm3.34
8529	→→𝜑→𝜒𝜑→→𝜑𝜒→𝜑𝜑	Subs [𝜓↗𝜒, 𝜒↗𝜑] into ax-2
8530	→→𝜑𝜒→𝜑𝜑	Modus ponens 13, 8529
8531	→→→𝜑𝜒→𝜑𝜑→¬¬𝜒→→𝜑𝜒→𝜑𝜑	Subs [𝜑↗→→𝜑𝜒→𝜑𝜑, 𝜓↗¬¬𝜒] into ax-1
8532	→¬¬𝜒→→𝜑𝜒→𝜑𝜑	Modus ponens 8530, 8531
8533	→→¬¬𝜒→→𝜑𝜒→𝜑𝜑→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑𝜑	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜑] into ax-2
8534	→→¬¬𝜒→𝜑𝜒→¬¬𝜒→𝜑𝜑	Modus ponens 8532, 8533
8535	→¬¬𝜒→𝜑𝜑	Modus ponens 7398, 8534
8536	→→¬¬𝜒→𝜑𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
8537	→→¬¬𝜒𝜑→¬¬𝜒𝜑	Modus ponens 8535, 8536
8538	→→→¬¬𝜒𝜑→¬¬𝜒𝜑→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑	Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒𝜑, 𝜓↗𝜑] into ax-1
8539	→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑	Modus ponens 8537, 8538
8540	→→𝜑→→¬¬𝜒𝜑→¬¬𝜒𝜑→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒𝜑	Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒𝜑] into ax-2
8541	→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒𝜑	Modus ponens 8539, 8540
8542	→→𝜑¬¬𝜑→¬¬𝜒→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜒] into ax-1
8543	→¬¬𝜒→𝜑¬¬𝜑	Modus ponens notnot, 8542
8544	→→¬¬𝜒→𝜑¬¬𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
8545	→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑	Modus ponens 8543, 8544
8546	→→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑	Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑, 𝜓↗𝜑] into ax-1
8547	→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑	Modus ponens 8545, 8546
8548	→→𝜑→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒¬¬𝜑	Subs [𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒¬¬𝜑] into ax-2
8549	→→𝜑→¬¬𝜒𝜑→𝜑→¬¬𝜒¬¬𝜑	Modus ponens 8547, 8548
8550	→𝜑→¬¬𝜒¬¬𝜑	Modus ponens 7406, 8549
8551	→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜑] into ax-3
8552	→→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒, 𝜓↗𝜑] into ax-1
8553	→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒	Modus ponens 8551, 8552
8554	→→𝜑→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→→𝜑→¬¬𝜒¬¬𝜑→𝜑→¬𝜑¬𝜒	Subs [𝜓↗→¬¬𝜒¬¬𝜑, 𝜒↗→¬𝜑¬𝜒] into ax-2
8555	→→𝜑→¬¬𝜒¬¬𝜑→𝜑→¬𝜑¬𝜒	Modus ponens 8553, 8554
8556	→𝜑→¬𝜑¬𝜒	Modus ponens 8550, 8555
8557	→→𝜑→¬𝜑¬𝜒→→𝜑¬𝜑→𝜑¬𝜒	Subs [𝜓↗¬𝜑, 𝜒↗¬𝜒] into ax-2
8558	→→𝜑¬𝜑→𝜑¬𝜒	Modus ponens 8556, 8557
8559	→→→𝜑¬𝜑→𝜑¬𝜒→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒	Subs [𝜑↗→→𝜑¬𝜑→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8560	→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒	Modus ponens 8558, 8559
8561	→→¬𝜑→→𝜑¬𝜑→𝜑¬𝜒→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜑, 𝜒↗→𝜑¬𝜒] into ax-2
8562	→→¬𝜑→𝜑¬𝜑→¬𝜑→𝜑¬𝜒	Modus ponens 8560, 8561
8563	→¬𝜑→𝜑¬𝜒	Modus ponens 414, 8562
8564	→→¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8565	→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 7440, 8564
8566	→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8567	→→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Subs [𝜑↗→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
8568	→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Modus ponens 8566, 8567
8569	→→¬¬¬→𝜑¬𝜒→¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗→¬𝜑¬→𝜑¬𝜒] into ax-2
8570	→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Modus ponens 8568, 8569
8571	→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Modus ponens 7443, 8570
8572	→→¬𝜑→¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗¬→𝜑¬𝜒, 𝜒↗¬→𝜑¬𝜒] into ax-2
8573	→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Modus ponens 8565, 8572
8574	→→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Subs [𝜑↗→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
8575	→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Modus ponens 8573, 8574
8576	→→¬¬¬→𝜑¬𝜒→→¬𝜑¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗→¬𝜑¬→𝜑¬𝜒, 𝜒↗→¬𝜑¬→𝜑¬𝜒] into ax-2
8577	→→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒	Modus ponens 8575, 8576
8578	→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→𝜑¬𝜒] into ax-1
8579	→→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
8580	→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑	Modus ponens 8578, 8579
8581	→→¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜒¬𝜑] into ax-2
8582	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑	Modus ponens 8580, 8581
8583	→→¬¬¬→𝜑¬𝜒→¬𝜑¬→𝜑¬𝜒→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬¬¬→𝜑¬𝜒, 𝜓↗¬𝜑, 𝜒↗¬→𝜑¬𝜒] into ax-2
8584	→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 8571, 8583
8585	→→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8586	→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 8584, 8585
8587	→→¬𝜑→→¬¬¬→𝜑¬𝜒¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜒¬𝜑, 𝜒↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒] into ax-2
8588	→→¬𝜑→¬¬¬→𝜑¬𝜒¬𝜑→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 8586, 8587
8589	→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒	Modus ponens 8578, 8588
8590	→→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒, 𝜓↗¬𝜑] into ax-1
8591	→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒	Modus ponens 7468, 8590
8592	→→¬𝜑→→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒, 𝜒↗→→𝜑¬𝜒¬¬→𝜑¬𝜒] into ax-2
8593	→→¬𝜑→¬¬¬→𝜑¬𝜒¬→𝜑¬𝜒→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒	Modus ponens 8591, 8592
8594	→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒	Modus ponens 8589, 8593
8595	→→¬𝜑→→𝜑¬𝜒¬¬→𝜑¬𝜒→→¬𝜑→𝜑¬𝜒→¬𝜑¬¬→𝜑¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→𝜑¬𝜒, 𝜒↗¬¬→𝜑¬𝜒] into ax-2
8596	→→¬𝜑→𝜑¬𝜒→¬𝜑¬¬→𝜑¬𝜒	Modus ponens 8594, 8595
8597	→¬𝜑¬¬→𝜑¬𝜒	Modus ponens 8563, 8596
8598	→→¬𝜑¬¬→𝜑¬𝜒→¬→𝜑¬𝜒𝜑	Subs [𝜓↗¬→𝜑¬𝜒] into ax-3
8599	→¬→𝜑¬𝜒𝜑	Modus ponens 8597, 8598
8600	→→¬→𝜑¬𝜒𝜑→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑	Subs [𝜑↗→¬→𝜑¬𝜒𝜑, 𝜓↗⋀𝜑𝜒] into ax-1
8601	→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑	Modus ponens 8599, 8600
8602	→→⋀𝜑𝜒→¬→𝜑¬𝜒𝜑→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒𝜑	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗𝜑] into ax-2
8603	→→⋀𝜑𝜒¬→𝜑¬𝜒→⋀𝜑𝜒𝜑	Modus ponens 8601, 8602
8604	→⋀𝜑𝜒𝜑	Modus ponens 7480, 8603
8605	→↔¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒⋀𝜑𝜒	Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜒] into biimp
8606	→¬→𝜑¬𝜒⋀𝜑𝜒	Modus ponens 6605, 8605
8607	→→⋀𝜑𝜒𝜑→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑	Subs [𝜑↗→⋀𝜑𝜒𝜑, 𝜓↗¬→𝜑¬𝜒] into ax-1
8608	→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑	Modus ponens 8604, 8607
8609	→→¬→𝜑¬𝜒→⋀𝜑𝜒𝜑→→¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒𝜑	Subs [𝜑↗¬→𝜑¬𝜒, 𝜓↗⋀𝜑𝜒, 𝜒↗𝜑] into ax-2
8610	→→¬→𝜑¬𝜒⋀𝜑𝜒→¬→𝜑¬𝜒𝜑	Modus ponens 8608, 8609
8611	→𝜑→𝜒¬→𝜑¬𝜒	Subs [𝜓↗𝜒] into pm3.2im
8612	→→¬→𝜑¬𝜒𝜑→𝜒→¬→𝜑¬𝜒𝜑	Subs [𝜑↗→¬→𝜑¬𝜒𝜑, 𝜓↗𝜒] into ax-1
8613	→𝜒→¬→𝜑¬𝜒𝜑	Modus ponens 8599, 8612
8614	→→𝜒→¬→𝜑¬𝜒𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑	Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬𝜒, 𝜒↗𝜑] into ax-2
8615	→→𝜒¬→𝜑¬𝜒→𝜒𝜑	Modus ponens 8613, 8614
8616	→→→𝜒¬→𝜑¬𝜒→𝜒𝜑→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑	Subs [𝜑↗→→𝜒¬→𝜑¬𝜒→𝜒𝜑, 𝜓↗𝜑] into ax-1
8617	→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑	Modus ponens 8615, 8616
8618	→→𝜑→→𝜒¬→𝜑¬𝜒→𝜒𝜑→→𝜑→𝜒¬→𝜑¬𝜒→𝜑→𝜒𝜑	Subs [𝜓↗→𝜒¬→𝜑¬𝜒, 𝜒↗→𝜒𝜑] into ax-2
8619	→→𝜑→𝜒¬→𝜑¬𝜒→𝜑→𝜒𝜑	Modus ponens 8617, 8618
8620	→→→𝜑𝜒→𝜑𝜑→𝜒→→𝜑𝜒→𝜑𝜑	Subs [𝜑↗→→𝜑𝜒→𝜑𝜑, 𝜓↗𝜒] into ax-1
8621	→𝜒→→𝜑𝜒→𝜑𝜑	Modus ponens 8530, 8620
8622	→→𝜒→→𝜑𝜒→𝜑𝜑→→𝜒→𝜑𝜒→𝜒→𝜑𝜑	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑𝜑] into ax-2
8623	→→𝜒→𝜑𝜒→𝜒→𝜑𝜑	Modus ponens 8621, 8622
8624	→𝜒→𝜑𝜑	Modus ponens 1834, 8623
8625	→→𝜑→𝜒𝜑→⋀𝜑𝜓→𝜑→𝜒𝜑	Subs [𝜑↗→𝜑→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8626	→⋀𝜑𝜓→𝜑→𝜒𝜑	Modus ponens 13, 8625
8627	→→⋀𝜑𝜓→𝜑→𝜒𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜒𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜒𝜑] into ax-2
8628	→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜒𝜑	Modus ponens 8626, 8627
8629	→⋀𝜑𝜓→𝜒𝜑	Modus ponens simpl, 8628
8630	→→𝜒→𝜑𝜑→→𝜒𝜑→𝜒𝜑	Subs [𝜑↗𝜒, 𝜓↗𝜑, 𝜒↗𝜑] into ax-2
8631	→→𝜒𝜑→𝜒𝜑	Modus ponens 8624, 8630
8632	→→→𝜒𝜑→𝜒𝜑→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑	Subs [𝜑↗→→𝜒𝜑→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8633	→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑	Modus ponens 8631, 8632
8634	→→⋀𝜑𝜓→→𝜒𝜑→𝜒𝜑→→⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→𝜒𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒𝜑, 𝜒↗→𝜒𝜑] into ax-2
8635	→→⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→𝜒𝜑	Modus ponens 8633, 8634
8636	→→𝜒→⋀𝜑𝜓𝜒→𝜒→𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
8637	→𝜒→𝜒→⋀𝜑𝜓𝜒	Modus ponens 5154, 8636
8638	→→𝜒→𝜒→⋀𝜑𝜓𝜒→→𝜒𝜒→𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
8639	→→𝜒𝜒→𝜒→⋀𝜑𝜓𝜒	Modus ponens 8637, 8638
8640	→→⋀𝜑𝜓→𝜒𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜑] into ax-2
8641	→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑	Modus ponens 8629, 8640
8642	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑	Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑, 𝜓↗𝜒] into ax-1
8643	→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑	Modus ponens 8641, 8642
8644	→→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜑	Subs [𝜑↗𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
8645	→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜑	Modus ponens 8643, 8644
8646	→𝜒→⋀𝜑𝜓𝜑	Modus ponens 5154, 8645
8647	→⋀𝜑𝜓→𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ax-1
8648	→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓	Subs [𝜑↗→⋀𝜑𝜓→𝜒⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8649	→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓	Modus ponens 8647, 8648
8650	→→⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜒⋀𝜑𝜓] into ax-2
8651	→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜒⋀𝜑𝜓	Modus ponens 8649, 8650
8652	→→𝜒→⋀𝜑𝜓𝜑→→𝜒⋀𝜑𝜓→𝜒𝜑	Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
8653	→→𝜒⋀𝜑𝜓→𝜒𝜑	Modus ponens 8646, 8652
8654	→→→𝜒⋀𝜑𝜓→𝜒𝜑→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑	Subs [𝜑↗→→𝜒⋀𝜑𝜓→𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8655	→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑	Modus ponens 8653, 8654
8656	→→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜑→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒⋀𝜑𝜓, 𝜒↗→𝜒𝜑] into ax-2
8657	→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜑	Modus ponens 8655, 8656
8658	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑	Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑, 𝜓↗¬¬𝜒] into ax-1
8659	→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑	Modus ponens 8641, 8658
8660	→→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜑→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜑	Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
8661	→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜑	Modus ponens 8659, 8660
8662	→¬¬𝜒→⋀𝜑𝜓𝜑	Modus ponens 5159, 8661
8663	→→¬¬𝜒→⋀𝜑𝜓𝜑→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑	Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
8664	→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑	Modus ponens 8662, 8663
8665	→→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑	Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8666	→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑	Modus ponens 8664, 8665
8667	→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜑→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒𝜑] into ax-2
8668	→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜑	Modus ponens 8666, 8667
8669	→⋀𝜑𝜓→¬¬𝜒𝜑	Modus ponens 5167, 8668
8670	→→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑	Subs [𝜑↗→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8671	→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑	Modus ponens 8545, 8670
8672	→→⋀𝜑𝜓→→¬¬𝜒𝜑→¬¬𝜒¬¬𝜑→→⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→¬¬𝜒¬¬𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒𝜑, 𝜒↗→¬¬𝜒¬¬𝜑] into ax-2
8673	→→⋀𝜑𝜓→¬¬𝜒𝜑→⋀𝜑𝜓→¬¬𝜒¬¬𝜑	Modus ponens 8671, 8672
8674	→⋀𝜑𝜓→¬¬𝜒¬¬𝜑	Modus ponens 8669, 8673
8675	→→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
8676	→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒	Modus ponens 8551, 8675
8677	→→⋀𝜑𝜓→→¬¬𝜒¬¬𝜑→¬𝜑¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬𝜑, 𝜒↗→¬𝜑¬𝜒] into ax-2
8678	→→⋀𝜑𝜓→¬¬𝜒¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜒	Modus ponens 8676, 8677
8679	→⋀𝜑𝜓→¬𝜑¬𝜒	Modus ponens 8674, 8678
8680	→¬𝜑→⋀𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
8681	→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑	Subs [𝜑↗→¬𝜑→⋀𝜑𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
8682	→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑	Modus ponens 8680, 8681
8683	→→¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜑] into ax-2
8684	→→¬𝜑¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜑	Modus ponens 8682, 8683
8685	→→⋀𝜑𝜓→¬𝜑¬𝜒→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜒] into ax-2
8686	→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 8679, 8685
8687	→→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8688	→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 8686, 8687
8689	→→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜒→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
8690	→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 8688, 8689
8691	→¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 8680, 8690
8692	→→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8693	→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5208, 8692
8694	→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8695	→→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8696	→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Modus ponens 8694, 8695
8697	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜒] into ax-2
8698	→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Modus ponens 8696, 8697
8699	→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Modus ponens 5211, 8698
8700	→→¬𝜑→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8701	→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Modus ponens 8693, 8700
8702	→→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8703	→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Modus ponens 8701, 8702
8704	→→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬𝜑¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜒] into ax-2
8705	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒	Modus ponens 8703, 8704
8706	→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8707	→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
8708	→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑	Modus ponens 8706, 8707
8709	→→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑] into ax-2
8710	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑	Modus ponens 8708, 8709
8711	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜑¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8712	→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8699, 8711
8713	→→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8714	→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8712, 8713
8715	→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
8716	→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8714, 8715
8717	→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8706, 8716
8718	→→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜑] into ax-1
8719	→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 5236, 8718
8720	→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8721	→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8719, 8720
8722	→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8717, 8721
8723	→→¬𝜑→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8724	→→¬𝜑→⋀𝜑𝜓¬𝜒→¬𝜑¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8722, 8723
8725	→¬𝜑¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8691, 8724
8726	→→¬𝜑¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒𝜑	Subs [𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3
8727	→¬→⋀𝜑𝜓¬𝜒𝜑	Modus ponens 8725, 8726
8728	→→¬→⋀𝜑𝜓¬𝜒𝜑→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8729	→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑	Modus ponens 8727, 8728
8730	→→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜑→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗𝜑] into ax-2
8731	→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 8729, 8730
8732	→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 5248, 8731	simpll
8733	→→𝜓→𝜒𝜓→→𝜓𝜒→𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into ax-2
8734	→→𝜓𝜒→𝜓𝜓	Modus ponens 5350, 8733
8735	→→→𝜓𝜒→𝜓𝜓→¬¬𝜒→→𝜓𝜒→𝜓𝜓	Subs [𝜑↗→→𝜓𝜒→𝜓𝜓, 𝜓↗¬¬𝜒] into ax-1
8736	→¬¬𝜒→→𝜓𝜒→𝜓𝜓	Modus ponens 8734, 8735
8737	→→¬¬𝜒→→𝜓𝜒→𝜓𝜓→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜓	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜓] into ax-2
8738	→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜓	Modus ponens 8736, 8737
8739	→¬¬𝜒→𝜓𝜓	Modus ponens 5367, 8738
8740	→→¬¬𝜒→𝜓𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓	Subs [𝜑↗¬¬𝜒, 𝜒↗𝜓] into ax-2
8741	→→¬¬𝜒𝜓→¬¬𝜒𝜓	Modus ponens 8739, 8740
8742	→→→¬¬𝜒𝜓→¬¬𝜒𝜓→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓	Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒𝜓] into ax-1
8743	→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓	Modus ponens 8741, 8742
8744	→→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜓→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2
8745	→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜓	Modus ponens 8743, 8744
8746	→→𝜓¬¬𝜓→¬¬𝜒→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜒] into ax-1
8747	→¬¬𝜒→𝜓¬¬𝜓	Modus ponens 448, 8746
8748	→→¬¬𝜒→𝜓¬¬𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓	Subs [𝜑↗¬¬𝜒, 𝜒↗¬¬𝜓] into ax-2
8749	→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓	Modus ponens 8747, 8748
8750	→→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓	Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓] into ax-1
8751	→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓	Modus ponens 8749, 8750
8752	→→𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒¬¬𝜓	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒¬¬𝜓] into ax-2
8753	→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒¬¬𝜓	Modus ponens 8751, 8752
8754	→𝜓→¬¬𝜒¬¬𝜓	Modus ponens 5375, 8753
8755	→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜓] into ax-3
8756	→→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒] into ax-1
8757	→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒	Modus ponens 8755, 8756
8758	→→𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→→𝜓→¬¬𝜒¬¬𝜓→𝜓→¬𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬𝜓, 𝜒↗→¬𝜓¬𝜒] into ax-2
8759	→→𝜓→¬¬𝜒¬¬𝜓→𝜓→¬𝜓¬𝜒	Modus ponens 8757, 8758
8760	→𝜓→¬𝜓¬𝜒	Modus ponens 8754, 8759
8761	→→𝜓→¬𝜓¬𝜒→→𝜓¬𝜓→𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜒] into ax-2
8762	→→𝜓¬𝜓→𝜓¬𝜒	Modus ponens 8760, 8761
8763	→→→𝜓¬𝜓→𝜓¬𝜒→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒	Subs [𝜑↗→→𝜓¬𝜓→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8764	→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒	Modus ponens 8762, 8763
8765	→→¬𝜓→→𝜓¬𝜓→𝜓¬𝜒→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜓, 𝜒↗→𝜓¬𝜒] into ax-2
8766	→→¬𝜓→𝜓¬𝜓→¬𝜓→𝜓¬𝜒	Modus ponens 8764, 8765
8767	→¬𝜓→𝜓¬𝜒	Modus ponens 5845, 8766
8768	→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8769	→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5416, 8768
8770	→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8771	→→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
8772	→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Modus ponens 8770, 8771
8773	→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬𝜓¬→𝜓¬𝜒] into ax-2
8774	→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Modus ponens 8772, 8773
8775	→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Modus ponens 5419, 8774
8776	→→¬𝜓→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
8777	→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Modus ponens 8769, 8776
8778	→→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Subs [𝜑↗→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
8779	→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Modus ponens 8777, 8778
8780	→→¬¬¬→𝜓¬𝜒→→¬𝜓¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬𝜓¬→𝜓¬𝜒, 𝜒↗→¬𝜓¬→𝜓¬𝜒] into ax-2
8781	→→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒	Modus ponens 8779, 8780
8782	→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
8783	→→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
8784	→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓	Modus ponens 8782, 8783
8785	→→¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜒¬𝜓] into ax-2
8786	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓	Modus ponens 8784, 8785
8787	→→¬¬¬→𝜓¬𝜒→¬𝜓¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬𝜓, 𝜒↗¬→𝜓¬𝜒] into ax-2
8788	→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 8775, 8787
8789	→→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8790	→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 8788, 8789
8791	→→¬𝜓→→¬¬¬→𝜓¬𝜒¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜒¬𝜓, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
8792	→→¬𝜓→¬¬¬→𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 8790, 8791
8793	→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 8782, 8792
8794	→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8795	→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 5444, 8794
8796	→→¬𝜓→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
8797	→→¬𝜓→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 8795, 8796
8798	→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 8793, 8797
8799	→→¬𝜓→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜓→𝜓¬𝜒→¬𝜓¬¬→𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
8800	→→¬𝜓→𝜓¬𝜒→¬𝜓¬¬→𝜓¬𝜒	Modus ponens 8798, 8799
8801	→¬𝜓¬¬→𝜓¬𝜒	Modus ponens 8767, 8800
8802	→→¬𝜓¬¬→𝜓¬𝜒→¬→𝜓¬𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜓¬𝜒] into ax-3
8803	→¬→𝜓¬𝜒𝜓	Modus ponens 8801, 8802
8804	→→¬→𝜓¬𝜒𝜓→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓	Subs [𝜑↗→¬→𝜓¬𝜒𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8805	→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓	Modus ponens 8803, 8804
8806	→→⋀𝜓𝜒→¬→𝜓¬𝜒𝜓→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗𝜓] into ax-2
8807	→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜓	Modus ponens 8805, 8806
8808	→→⋀𝜓𝜒𝜓→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓	Subs [𝜑↗→⋀𝜓𝜒𝜓, 𝜓↗¬→𝜓¬𝜒] into ax-1
8809	→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓	Modus ponens 6072, 8808
8810	→→¬→𝜓¬𝜒→⋀𝜓𝜒𝜓→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒𝜓	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
8811	→→¬→𝜓¬𝜒⋀𝜓𝜒→¬→𝜓¬𝜒𝜓	Modus ponens 8809, 8810
8812	→→¬→𝜓¬𝜒𝜓→𝜒→¬→𝜓¬𝜒𝜓	Subs [𝜑↗→¬→𝜓¬𝜒𝜓, 𝜓↗𝜒] into ax-1
8813	→𝜒→¬→𝜓¬𝜒𝜓	Modus ponens 8803, 8812
8814	→→𝜒→¬→𝜓¬𝜒𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗𝜓] into ax-2
8815	→→𝜒¬→𝜓¬𝜒→𝜒𝜓	Modus ponens 8813, 8814
8816	→→→𝜒¬→𝜓¬𝜒→𝜒𝜓→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓	Subs [𝜑↗→→𝜒¬→𝜓¬𝜒→𝜒𝜓] into ax-1
8817	→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓	Modus ponens 8815, 8816
8818	→→𝜓→→𝜒¬→𝜓¬𝜒→𝜒𝜓→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗→𝜒¬→𝜓¬𝜒, 𝜒↗→𝜒𝜓] into ax-2
8819	→→𝜓→𝜒¬→𝜓¬𝜒→𝜓→𝜒𝜓	Modus ponens 8817, 8818
8820	→→→𝜓𝜒→𝜓𝜓→𝜒→→𝜓𝜒→𝜓𝜓	Subs [𝜑↗→→𝜓𝜒→𝜓𝜓, 𝜓↗𝜒] into ax-1
8821	→𝜒→→𝜓𝜒→𝜓𝜓	Modus ponens 8734, 8820
8822	→→𝜒→→𝜓𝜒→𝜓𝜓→→𝜒→𝜓𝜒→𝜒→𝜓𝜓	Subs [𝜑↗𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜓] into ax-2
8823	→→𝜒→𝜓𝜒→𝜒→𝜓𝜓	Modus ponens 8821, 8822
8824	→𝜒→𝜓𝜓	Modus ponens 5362, 8823
8825	→→𝜓→𝜒𝜓→⋀𝜑𝜓→𝜓→𝜒𝜓	Subs [𝜑↗→𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8826	→⋀𝜑𝜓→𝜓→𝜒𝜓	Modus ponens 5350, 8825
8827	→→⋀𝜑𝜓→𝜓→𝜒𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜒𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2
8828	→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜒𝜓	Modus ponens 8826, 8827
8829	→⋀𝜑𝜓→𝜒𝜓	Modus ponens simpr, 8828
8830	→→𝜒→𝜓𝜓→→𝜒𝜓→𝜒𝜓	Subs [𝜑↗𝜒, 𝜒↗𝜓] into ax-2
8831	→→𝜒𝜓→𝜒𝜓	Modus ponens 8824, 8830
8832	→→→𝜒𝜓→𝜒𝜓→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓	Subs [𝜑↗→→𝜒𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8833	→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓	Modus ponens 8831, 8832
8834	→→⋀𝜑𝜓→→𝜒𝜓→𝜒𝜓→→⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→𝜒𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜓] into ax-2
8835	→→⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→𝜒𝜓	Modus ponens 8833, 8834
8836	→→⋀𝜑𝜓→𝜒𝜓→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into ax-2
8837	→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓	Modus ponens 8829, 8836
8838	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓	Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗𝜒] into ax-1
8839	→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓	Modus ponens 8837, 8838
8840	→→𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜓	Subs [𝜑↗𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
8841	→→𝜒→⋀𝜑𝜓𝜒→𝜒→⋀𝜑𝜓𝜓	Modus ponens 8839, 8840
8842	→𝜒→⋀𝜑𝜓𝜓	Modus ponens 5154, 8841
8843	→→𝜒→⋀𝜑𝜓𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
8844	→→𝜒⋀𝜑𝜓→𝜒𝜓	Modus ponens 8842, 8843
8845	→→→𝜒⋀𝜑𝜓→𝜒𝜓→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓	Subs [𝜑↗→→𝜒⋀𝜑𝜓→𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8846	→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓	Modus ponens 8844, 8845
8847	→→⋀𝜑𝜓→→𝜒⋀𝜑𝜓→𝜒𝜓→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜒⋀𝜑𝜓, 𝜒↗→𝜒𝜓] into ax-2
8848	→→⋀𝜑𝜓→𝜒⋀𝜑𝜓→⋀𝜑𝜓→𝜒𝜓	Modus ponens 8846, 8847
8849	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓	Subs [𝜑↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗¬¬𝜒] into ax-1
8850	→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓	Modus ponens 8837, 8849
8851	→→¬¬𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜓→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜓	Subs [𝜑↗¬¬𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
8852	→→¬¬𝜒→⋀𝜑𝜓𝜒→¬¬𝜒→⋀𝜑𝜓𝜓	Modus ponens 8850, 8851
8853	→¬¬𝜒→⋀𝜑𝜓𝜓	Modus ponens 5159, 8852
8854	→→¬¬𝜒→⋀𝜑𝜓𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓	Subs [𝜑↗¬¬𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
8855	→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓	Modus ponens 8853, 8854
8856	→→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓	Subs [𝜑↗→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8857	→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓	Modus ponens 8855, 8856
8858	→→⋀𝜑𝜓→→¬¬𝜒⋀𝜑𝜓→¬¬𝜒𝜓→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒⋀𝜑𝜓, 𝜒↗→¬¬𝜒𝜓] into ax-2
8859	→→⋀𝜑𝜓→¬¬𝜒⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜒𝜓	Modus ponens 8857, 8858
8860	→⋀𝜑𝜓→¬¬𝜒𝜓	Modus ponens 5167, 8859
8861	→→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓	Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8862	→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓	Modus ponens 8749, 8861
8863	→→⋀𝜑𝜓→→¬¬𝜒𝜓→¬¬𝜒¬¬𝜓→→⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→¬¬𝜒¬¬𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒¬¬𝜓] into ax-2
8864	→→⋀𝜑𝜓→¬¬𝜒𝜓→⋀𝜑𝜓→¬¬𝜒¬¬𝜓	Modus ponens 8862, 8863
8865	→⋀𝜑𝜓→¬¬𝜒¬¬𝜓	Modus ponens 8860, 8864
8866	→→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
8867	→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒	Modus ponens 8755, 8866
8868	→→⋀𝜑𝜓→→¬¬𝜒¬¬𝜓→¬𝜓¬𝜒→→⋀𝜑𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜒¬¬𝜓, 𝜒↗→¬𝜓¬𝜒] into ax-2
8869	→→⋀𝜑𝜓→¬¬𝜒¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜒	Modus ponens 8867, 8868
8870	→⋀𝜑𝜓→¬𝜓¬𝜒	Modus ponens 8865, 8869
8871	→¬𝜓→⋀𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
8872	→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓	Subs [𝜑↗→¬𝜓→⋀𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
8873	→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓	Modus ponens 8871, 8872
8874	→→¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜓] into ax-2
8875	→→¬𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜓	Modus ponens 8873, 8874
8876	→→⋀𝜑𝜓→¬𝜓¬𝜒→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜒] into ax-2
8877	→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒	Modus ponens 8870, 8876
8878	→→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8879	→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒	Modus ponens 8877, 8878
8880	→→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜒→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
8881	→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜒	Modus ponens 8879, 8880
8882	→¬𝜓→⋀𝜑𝜓¬𝜒	Modus ponens 8871, 8881
8883	→→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8884	→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 5208, 8883
8885	→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8886	→→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8887	→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Modus ponens 8885, 8886
8888	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜒] into ax-2
8889	→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Modus ponens 8887, 8888
8890	→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Modus ponens 5211, 8889
8891	→→¬𝜓→¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8892	→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Modus ponens 8884, 8891
8893	→→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8894	→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Modus ponens 8892, 8893
8895	→→¬¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗→¬𝜓¬→⋀𝜑𝜓¬𝜒, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜒] into ax-2
8896	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒	Modus ponens 8894, 8895
8897	→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜒] into ax-1
8898	→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
8899	→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓	Modus ponens 8897, 8898
8900	→→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓] into ax-2
8901	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓	Modus ponens 8899, 8900
8902	→→¬¬¬→⋀𝜑𝜓¬𝜒→¬𝜓¬→⋀𝜑𝜓¬𝜒→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑𝜓¬𝜒] into ax-2
8903	→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8890, 8902
8904	→→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8905	→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8903, 8904
8906	→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒] into ax-2
8907	→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8905, 8906
8908	→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒	Modus ponens 8897, 8907
8909	→→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒, 𝜓↗¬𝜓] into ax-1
8910	→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 5236, 8909
8911	→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒, 𝜒↗→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8912	→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜒¬→⋀𝜑𝜓¬𝜒→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8910, 8911
8913	→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8908, 8912
8914	→→¬𝜓→→⋀𝜑𝜓¬𝜒¬¬→⋀𝜑𝜓¬𝜒→→¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓¬¬→⋀𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜒, 𝜒↗¬¬→⋀𝜑𝜓¬𝜒] into ax-2
8915	→→¬𝜓→⋀𝜑𝜓¬𝜒→¬𝜓¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8913, 8914
8916	→¬𝜓¬¬→⋀𝜑𝜓¬𝜒	Modus ponens 8882, 8915
8917	→→¬𝜓¬¬→⋀𝜑𝜓¬𝜒→¬→⋀𝜑𝜓¬𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜒] into ax-3
8918	→¬→⋀𝜑𝜓¬𝜒𝜓	Modus ponens 8916, 8917
8919	→→¬→⋀𝜑𝜓¬𝜒𝜓→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜒𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
8920	→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓	Modus ponens 8918, 8919
8921	→→⋀⋀𝜑𝜓𝜒→¬→⋀𝜑𝜓¬𝜒𝜓→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬→⋀𝜑𝜓¬𝜒, 𝜒↗𝜓] into ax-2
8922	→→⋀⋀𝜑𝜓𝜒¬→⋀𝜑𝜓¬𝜒→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 8920, 8921
8923	→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 5248, 8922	simplr
8924	→→𝜓→𝜑𝜓→⋀𝜓𝜒→𝜓→𝜑𝜓	Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8925	→⋀𝜓𝜒→𝜓→𝜑𝜓	Modus ponens 208, 8924
8926	→→⋀𝜓𝜒→𝜓→𝜑𝜓→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
8927	→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜑𝜓	Modus ponens 8925, 8926
8928	→⋀𝜓𝜒→𝜑𝜓	Modus ponens 6072, 8927
8929	↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into df-an
8930	→→𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑	Subs [𝜑↗→𝜑→⋀𝜓𝜒𝜑, 𝜓↗¬¬𝜑] into ax-1
8931	→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑	Modus ponens 5462, 8930
8932	→→¬¬𝜑→𝜑→⋀𝜓𝜒𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓𝜒𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀𝜓𝜒𝜑] into ax-2
8933	→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓𝜒𝜑	Modus ponens 8931, 8932
8934	→¬¬𝜑→⋀𝜓𝜒𝜑	Modus ponens notnotr, 8933
8935	→→⋀𝜓𝜒→𝜑𝜓→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
8936	→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓	Modus ponens 8928, 8935
8937	→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜑] into ax-1
8938	→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓	Modus ponens 8936, 8937
8939	→→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
8940	→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜓	Modus ponens 8938, 8939
8941	→¬¬𝜑→⋀𝜓𝜒𝜓	Modus ponens 8934, 8940
8942	→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1
8943	→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
8944	→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒	Modus ponens 8942, 8943
8945	→→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→¬¬𝜑⋀𝜓𝜒] into ax-2
8946	→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒	Modus ponens 8944, 8945
8947	→→¬¬𝜑→⋀𝜓𝜒𝜓→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓	Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
8948	→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓	Modus ponens 8941, 8947
8949	→→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓	Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8950	→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓	Modus ponens 8948, 8949
8951	→→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜓→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑𝜓] into ax-2
8952	→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜓	Modus ponens 8950, 8951
8953	→⋀𝜓𝜒→¬¬𝜑𝜓	Modus ponens 8942, 8952
8954	→→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Subs [𝜑↗→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8955	→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓	Modus ponens 488, 8954
8956	→→⋀𝜓𝜒→→¬¬𝜑𝜓→¬¬𝜑¬¬𝜓→→⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→¬¬𝜑¬¬𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑𝜓, 𝜒↗→¬¬𝜑¬¬𝜓] into ax-2
8957	→→⋀𝜓𝜒→¬¬𝜑𝜓→⋀𝜓𝜒→¬¬𝜑¬¬𝜓	Modus ponens 8955, 8956
8958	→⋀𝜓𝜒→¬¬𝜑¬¬𝜓	Modus ponens 8953, 8957
8959	→→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
8960	→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑	Modus ponens 494, 8959
8961	→→⋀𝜓𝜒→→¬¬𝜑¬¬𝜓→¬𝜓¬𝜑→→⋀𝜓𝜒→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑¬¬𝜓, 𝜒↗→¬𝜓¬𝜑] into ax-2
8962	→→⋀𝜓𝜒→¬¬𝜑¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜑	Modus ponens 8960, 8961
8963	→⋀𝜓𝜒→¬𝜓¬𝜑	Modus ponens 8958, 8962
8964	→¬𝜓→⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
8965	→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓	Subs [𝜑↗→¬𝜓→⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
8966	→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓	Modus ponens 8964, 8965
8967	→→¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜓] into ax-2
8968	→→¬𝜓¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜓	Modus ponens 8966, 8967
8969	→→⋀𝜓𝜒→¬𝜓¬𝜑→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜑] into ax-2
8970	→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑	Modus ponens 8963, 8969
8971	→→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
8972	→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑	Modus ponens 8970, 8971
8973	→→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜑→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2
8974	→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜑	Modus ponens 8972, 8973
8975	→¬𝜓→⋀𝜓𝜒¬𝜑	Modus ponens 8964, 8974
8976	→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑] into id
8977	→→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
8978	→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 8976, 8977
8979	→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑] into notnotr
8980	→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
8981	→→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
8982	→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Modus ponens 8980, 8981
8983	→→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜑] into ax-2
8984	→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Modus ponens 8982, 8983
8985	→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Modus ponens 8979, 8984
8986	→→¬𝜓→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
8987	→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Modus ponens 8978, 8986
8988	→→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
8989	→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Modus ponens 8987, 8988
8990	→→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→¬𝜓¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜑] into ax-2
8991	→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑	Modus ponens 8989, 8990
8992	→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
8993	→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓, 𝜓↗¬𝜓] into ax-1
8994	→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓	Modus ponens 8992, 8993
8995	→→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓] into ax-2
8996	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓	Modus ponens 8994, 8995
8997	→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜓¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
8998	→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 8985, 8997
8999	→→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
9000	→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 8998, 8999
9001	→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑] into ax-2
9002	→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 9000, 9001
9003	→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 8992, 9002
9004	→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜓𝜒¬𝜑] into ax-3
9005	→→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜓] into ax-1
9006	→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9004, 9005
9007	→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9008	→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9006, 9007
9009	→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9003, 9008
9010	→→¬𝜓→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓¬¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜑, 𝜒↗¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9011	→→¬𝜓→⋀𝜓𝜒¬𝜑→¬𝜓¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9009, 9010
9012	→¬𝜓¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 8975, 9011
9013	→→¬𝜓¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-3
9014	→¬→⋀𝜓𝜒¬𝜑𝜓	Modus ponens 9012, 9013
9015	→↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into biimp
9016	→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 8929, 9015
9017	→→¬→⋀𝜓𝜒¬𝜑𝜓→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜓, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-1
9018	→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓	Modus ponens 9014, 9017
9019	→→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓	Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗𝜓] into ax-2
9020	→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓	Modus ponens 9018, 9019
9021	→⋀⋀𝜓𝜒𝜑𝜓	Modus ponens 9016, 9020
9022	→↔⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into bicom1
9023	↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑	Modus ponens 8929, 9022
9024	→↔¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into biimp
9025	→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑	Modus ponens 9023, 9024
9026	→→⋀⋀𝜓𝜒𝜑𝜓→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓	Subs [𝜑↗→⋀⋀𝜓𝜒𝜑𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-1
9027	→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓	Modus ponens 9021, 9026
9028	→→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜓→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑, 𝜒↗𝜓] into ax-2
9029	→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜓	Modus ponens 9027, 9028
9030	→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into pm3.2im
9031	→→¬→⋀𝜓𝜒¬𝜑𝜓→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜓, 𝜓↗𝜑] into ax-1
9032	→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓	Modus ponens 9014, 9031
9033	→→𝜑→¬→⋀𝜓𝜒¬𝜑𝜓→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓	Subs [𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗𝜓] into ax-2
9034	→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓	Modus ponens 9032, 9033
9035	→→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
9036	→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓	Modus ponens 9034, 9035
9037	→→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜓→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→𝜑𝜓] into ax-2
9038	→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜓	Modus ponens 9036, 9037
9039	→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
9040	→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓	Modus ponens 8936, 9039
9041	→→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜓→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜓	Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
9042	→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜓	Modus ponens 9040, 9041
9043	→→→𝜑⋀𝜓𝜒→𝜑𝜓→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9044	→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 6076, 9043
9045	→→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜓→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
9046	→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜓	Modus ponens 9044, 9045
9047	→¬¬⋀𝜓𝜒→𝜑𝜓	Modus ponens 5479, 9046
9048	→→¬¬⋀𝜓𝜒→𝜑𝜓→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
9049	→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓	Modus ponens 9047, 9048
9050	→→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓	Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
9051	→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓	Modus ponens 9049, 9050
9052	→→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜓→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜓	Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜓] into ax-2
9053	→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜓	Modus ponens 9051, 9052
9054	→𝜑→¬¬⋀𝜓𝜒𝜓	Modus ponens 5487, 9053
9055	→→𝜓¬¬𝜓→¬¬⋀𝜓𝜒→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9056	→¬¬⋀𝜓𝜒→𝜓¬¬𝜓	Modus ponens 448, 9055
9057	→→¬¬⋀𝜓𝜒→𝜓¬¬𝜓→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜒↗¬¬𝜓] into ax-2
9058	→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓	Modus ponens 9056, 9057
9059	→→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓	Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓, 𝜓↗𝜑] into ax-1
9060	→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓	Modus ponens 9058, 9059
9061	→→𝜑→→¬¬⋀𝜓𝜒𝜓→¬¬⋀𝜓𝜒¬¬𝜓→→𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→¬¬⋀𝜓𝜒¬¬𝜓	Subs [𝜓↗→¬¬⋀𝜓𝜒𝜓, 𝜒↗→¬¬⋀𝜓𝜒¬¬𝜓] into ax-2
9062	→→𝜑→¬¬⋀𝜓𝜒𝜓→𝜑→¬¬⋀𝜓𝜒¬¬𝜓	Modus ponens 9060, 9061
9063	→𝜑→¬¬⋀𝜓𝜒¬¬𝜓	Modus ponens 9054, 9062
9064	→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-3
9065	→→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
9066	→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒	Modus ponens 9064, 9065
9067	→→𝜑→→¬¬⋀𝜓𝜒¬¬𝜓→¬𝜓¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→¬𝜓¬⋀𝜓𝜒	Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬𝜓, 𝜒↗→¬𝜓¬⋀𝜓𝜒] into ax-2
9068	→→𝜑→¬¬⋀𝜓𝜒¬¬𝜓→𝜑→¬𝜓¬⋀𝜓𝜒	Modus ponens 9066, 9067
9069	→𝜑→¬𝜓¬⋀𝜓𝜒	Modus ponens 9063, 9068
9070	→→𝜑→¬𝜓¬⋀𝜓𝜒→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒	Subs [𝜓↗¬𝜓, 𝜒↗¬⋀𝜓𝜒] into ax-2
9071	→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒	Modus ponens 9069, 9070
9072	→→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9073	→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒	Modus ponens 9071, 9072
9074	→→¬𝜓→→𝜑¬𝜓→𝜑¬⋀𝜓𝜒→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
9075	→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬⋀𝜓𝜒	Modus ponens 9073, 9074
9076	→¬𝜓→𝜑¬⋀𝜓𝜒	Modus ponens 609, 9075
9077	→→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9078	→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5528, 9077
9079	→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9080	→→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9081	→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Modus ponens 9079, 9080
9082	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜓¬→𝜑¬⋀𝜓𝜒] into ax-2
9083	→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Modus ponens 9081, 9082
9084	→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Modus ponens 5531, 9083
9085	→→¬𝜓→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9086	→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Modus ponens 9078, 9085
9087	→→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9088	→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Modus ponens 9086, 9087
9089	→→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬𝜓¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜓¬→𝜑¬⋀𝜓𝜒] into ax-2
9090	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒	Modus ponens 9088, 9089
9091	→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9092	→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
9093	→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓	Modus ponens 9091, 9092
9094	→→¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓] into ax-2
9095	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓	Modus ponens 9093, 9094
9096	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜓¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9097	→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9084, 9096
9098	→→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9099	→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9097, 9098
9100	→→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9101	→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜓→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9099, 9100
9102	→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9091, 9101
9103	→→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜓] into ax-1
9104	→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 5556, 9103
9105	→→¬𝜓→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9106	→→¬𝜓→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9104, 9105
9107	→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9102, 9106
9108	→→¬𝜓→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9109	→→¬𝜓→𝜑¬⋀𝜓𝜒→¬𝜓¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9107, 9108
9110	→¬𝜓¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9076, 9109
9111	→→¬𝜓¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3
9112	→¬→𝜑¬⋀𝜓𝜒𝜓	Modus ponens 9110, 9111
9113	→→¬→𝜑¬⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9114	→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓	Modus ponens 9112, 9113
9115	→→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
9116	→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9114, 9115
9117	→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 5568, 9116	simprl
9118	→⋀𝜑⋀𝜓𝜒𝜑	Subs [𝜓↗⋀𝜓𝜒] into simpl
9119	→→⋀𝜑𝜓𝜓→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓	Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-1
9120	→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓	Modus ponens simpr, 9119
9121	→→¬→𝜑¬𝜓→⋀𝜑𝜓𝜓→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
9122	→→¬→𝜑¬𝜓⋀𝜑𝜓→¬→𝜑¬𝜓𝜓	Modus ponens 9120, 9121
9123	→→¬→𝜑¬𝜓𝜓→𝜓→¬→𝜑¬𝜓𝜓	Subs [𝜑↗→¬→𝜑¬𝜓𝜓] into ax-1
9124	→𝜓→¬→𝜑¬𝜓𝜓	Modus ponens simprim, 9123
9125	→→𝜓→¬→𝜑¬𝜓𝜓→→𝜓¬→𝜑¬𝜓→𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗𝜓] into ax-2
9126	→→𝜓¬→𝜑¬𝜓→𝜓𝜓	Modus ponens 9124, 9125
9127	→→→𝜓¬→𝜑¬𝜓→𝜓𝜓→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓	Subs [𝜑↗→→𝜓¬→𝜑¬𝜓→𝜓𝜓, 𝜓↗𝜑] into ax-1
9128	→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓	Modus ponens 9126, 9127
9129	→→𝜑→→𝜓¬→𝜑¬𝜓→𝜓𝜓→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓𝜓	Subs [𝜓↗→𝜓¬→𝜑¬𝜓, 𝜒↗→𝜓𝜓] into ax-2
9130	→→𝜑→𝜓¬→𝜑¬𝜓→𝜑→𝜓𝜓	Modus ponens 9128, 9129
9131	→→𝜓→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓	Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9132	→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓	Modus ponens 208, 9131
9133	→→⋀𝜑⋀𝜓𝜒→𝜓→𝜑𝜓→→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
9134	→→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 9132, 9133
9135	→⋀𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens simprl, 9134
9136	→→→𝜑𝜓→𝜑𝜓→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9137	→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 24, 9136
9138	→→⋀𝜑⋀𝜓𝜒→→𝜑𝜓→𝜑𝜓→→⋀𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
9139	→→⋀𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 9137, 9138
9140	→𝜑→⋀𝜑⋀𝜓𝜒𝜑	Subs [𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9141	→→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑	Subs [𝜑↗→𝜑→⋀𝜑⋀𝜓𝜒𝜑, 𝜓↗𝜑] into ax-1
9142	→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑	Modus ponens 9140, 9141
9143	→→𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑→→𝜑𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑	Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜑] into ax-2
9144	→→𝜑𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜑	Modus ponens 9142, 9143
9145	→→⋀𝜑⋀𝜓𝜒→𝜑𝜓→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
9146	→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9135, 9145
9147	→→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
9148	→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9146, 9147
9149	→→𝜑→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒𝜓→→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜓↗→⋀𝜑⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
9150	→→𝜑→⋀𝜑⋀𝜓𝜒𝜑→𝜑→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9148, 9149
9151	→𝜑→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9140, 9150
9152	→→𝜑→⋀𝜑⋀𝜓𝜒𝜓→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗→𝜑→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9153	→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9151, 9152
9154	→→⋀𝜑⋀𝜓𝜒→𝜑→⋀𝜑⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
9155	→→⋀𝜑⋀𝜓𝜒𝜑→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9153, 9154
9156	→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9118, 9155
9157	→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
9158	→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 9156, 9157
9159	→→𝜒→𝜓𝜒→→𝜒𝜓→𝜒𝜒	Subs [𝜑↗𝜒] into ax-2
9160	→→𝜒𝜓→𝜒𝜒	Modus ponens 5362, 9159
9161	→→→𝜒𝜓→𝜒𝜒→¬¬𝜓→→𝜒𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜓→𝜒𝜒, 𝜓↗¬¬𝜓] into ax-1
9162	→¬¬𝜓→→𝜒𝜓→𝜒𝜒	Modus ponens 9160, 9161
9163	→→¬¬𝜓→→𝜒𝜓→𝜒𝜒→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜒] into ax-2
9164	→→¬¬𝜓→𝜒𝜓→¬¬𝜓→𝜒𝜒	Modus ponens 9162, 9163
9165	→¬¬𝜓→𝜒𝜒	Modus ponens 7002, 9164
9166	→→¬¬𝜓→𝜒𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒] into ax-2
9167	→→¬¬𝜓𝜒→¬¬𝜓𝜒	Modus ponens 9165, 9166
9168	→→→¬¬𝜓𝜒→¬¬𝜓𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒	Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓𝜒, 𝜓↗𝜒] into ax-1
9169	→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒	Modus ponens 9167, 9168
9170	→→𝜒→→¬¬𝜓𝜒→¬¬𝜓𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓𝜒] into ax-2
9171	→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓𝜒	Modus ponens 9169, 9170
9172	→𝜒¬¬𝜒	Subs [𝜑↗𝜒] into notnot
9173	→→𝜒¬¬𝜒→¬¬𝜓→𝜒¬¬𝜒	Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜓] into ax-1
9174	→¬¬𝜓→𝜒¬¬𝜒	Modus ponens 9172, 9173
9175	→→¬¬𝜓→𝜒¬¬𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9176	→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒	Modus ponens 9174, 9175
9177	→→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒	Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒, 𝜓↗𝜒] into ax-1
9178	→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒	Modus ponens 9176, 9177
9179	→→𝜒→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓¬¬𝜒	Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓¬¬𝜒] into ax-2
9180	→→𝜒→¬¬𝜓𝜒→𝜒→¬¬𝜓¬¬𝜒	Modus ponens 9178, 9179
9181	→𝜒→¬¬𝜓¬¬𝜒	Modus ponens 7010, 9180
9182	→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜒] into ax-3
9183	→→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓, 𝜓↗𝜒] into ax-1
9184	→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓	Modus ponens 9182, 9183
9185	→→𝜒→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→→𝜒→¬¬𝜓¬¬𝜒→𝜒→¬𝜒¬𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬𝜓¬¬𝜒, 𝜒↗→¬𝜒¬𝜓] into ax-2
9186	→→𝜒→¬¬𝜓¬¬𝜒→𝜒→¬𝜒¬𝜓	Modus ponens 9184, 9185
9187	→𝜒→¬𝜒¬𝜓	Modus ponens 9181, 9186
9188	→¬𝜒¬𝜒	Subs [𝜑↗¬𝜒] into id
9189	→¬𝜒→𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗𝜒] into ax-1
9190	→→¬𝜒→𝜒¬𝜒→¬𝜒→¬𝜒→𝜒¬𝜒	Subs [𝜑↗→¬𝜒→𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9191	→¬𝜒→¬𝜒→𝜒¬𝜒	Modus ponens 9189, 9190
9192	→→¬𝜒→¬𝜒→𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜒¬𝜒] into ax-2
9193	→→¬𝜒¬𝜒→¬𝜒→𝜒¬𝜒	Modus ponens 9191, 9192
9194	→→𝜒→¬𝜒¬𝜓→→𝜒¬𝜒→𝜒¬𝜓	Subs [𝜑↗𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜓] into ax-2
9195	→→𝜒¬𝜒→𝜒¬𝜓	Modus ponens 9187, 9194
9196	→→→𝜒¬𝜒→𝜒¬𝜓→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓	Subs [𝜑↗→→𝜒¬𝜒→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9197	→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓	Modus ponens 9195, 9196
9198	→→¬𝜒→→𝜒¬𝜒→𝜒¬𝜓→→¬𝜒→𝜒¬𝜒→¬𝜒→𝜒¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→𝜒¬𝜒, 𝜒↗→𝜒¬𝜓] into ax-2
9199	→→¬𝜒→𝜒¬𝜒→¬𝜒→𝜒¬𝜓	Modus ponens 9197, 9198
9200	→¬𝜒→𝜒¬𝜓	Modus ponens 9189, 9199
9201	→→¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗→¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9202	→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 7051, 9201
9203	→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9204	→→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Subs [𝜑↗→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
9205	→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Modus ponens 9203, 9204
9206	→→¬¬¬→𝜒¬𝜓→¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬→𝜒¬𝜓, 𝜒↗→¬𝜒¬→𝜒¬𝜓] into ax-2
9207	→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Modus ponens 9205, 9206
9208	→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Modus ponens 7054, 9207
9209	→→¬𝜒→¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜒¬𝜓, 𝜒↗¬→𝜒¬𝜓] into ax-2
9210	→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Modus ponens 9202, 9209
9211	→→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Subs [𝜑↗→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
9212	→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Modus ponens 9210, 9211
9213	→→¬¬¬→𝜒¬𝜓→→¬𝜒¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗→¬𝜒¬→𝜒¬𝜓, 𝜒↗→¬𝜒¬→𝜒¬𝜓] into ax-2
9214	→→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓	Modus ponens 9212, 9213
9215	→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜒¬𝜓] into ax-1
9216	→→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9217	→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒	Modus ponens 9215, 9216
9218	→→¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬𝜒] into ax-2
9219	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒	Modus ponens 9217, 9218
9220	→→¬¬¬→𝜒¬𝜓→¬𝜒¬→𝜒¬𝜓→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗¬¬¬→𝜒¬𝜓, 𝜓↗¬𝜒, 𝜒↗¬→𝜒¬𝜓] into ax-2
9221	→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 9208, 9220
9222	→→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9223	→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 9221, 9222
9224	→→¬𝜒→→¬¬¬→𝜒¬𝜓¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬𝜒, 𝜒↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓] into ax-2
9225	→→¬𝜒→¬¬¬→𝜒¬𝜓¬𝜒→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 9223, 9224
9226	→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓	Modus ponens 9215, 9225
9227	→→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓, 𝜓↗¬𝜒] into ax-1
9228	→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓	Modus ponens 7079, 9227
9229	→→¬𝜒→→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓, 𝜒↗→→𝜒¬𝜓¬¬→𝜒¬𝜓] into ax-2
9230	→→¬𝜒→¬¬¬→𝜒¬𝜓¬→𝜒¬𝜓→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓	Modus ponens 9228, 9229
9231	→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓	Modus ponens 9226, 9230
9232	→→¬𝜒→→𝜒¬𝜓¬¬→𝜒¬𝜓→→¬𝜒→𝜒¬𝜓→¬𝜒¬¬→𝜒¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→𝜒¬𝜓, 𝜒↗¬¬→𝜒¬𝜓] into ax-2
9233	→→¬𝜒→𝜒¬𝜓→¬𝜒¬¬→𝜒¬𝜓	Modus ponens 9231, 9232
9234	→¬𝜒¬¬→𝜒¬𝜓	Modus ponens 9200, 9233
9235	→→¬𝜒¬¬→𝜒¬𝜓→¬→𝜒¬𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-3
9236	→¬→𝜒¬𝜓𝜒	Modus ponens 9234, 9235
9237	→→¬→𝜒¬𝜓𝜒→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒	Subs [𝜑↗→¬→𝜒¬𝜓𝜒, 𝜓↗⋀𝜒𝜓] into ax-1
9238	→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒	Modus ponens 9236, 9237
9239	→→⋀𝜒𝜓→¬→𝜒¬𝜓𝜒→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓𝜒	Subs [𝜑↗⋀𝜒𝜓, 𝜓↗¬→𝜒¬𝜓] into ax-2
9240	→→⋀𝜒𝜓¬→𝜒¬𝜓→⋀𝜒𝜓𝜒	Modus ponens 9238, 9239
9241	→⋀𝜒𝜓𝜒	Modus ponens 7091, 9240
9242	→→⋀𝜒𝜓𝜒→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒	Subs [𝜑↗→⋀𝜒𝜓𝜒, 𝜓↗¬→𝜒¬𝜓] into ax-1
9243	→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒	Modus ponens 9241, 9242
9244	→→¬→𝜒¬𝜓→⋀𝜒𝜓𝜒→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓𝜒	Subs [𝜑↗¬→𝜒¬𝜓, 𝜓↗⋀𝜒𝜓] into ax-2
9245	→→¬→𝜒¬𝜓⋀𝜒𝜓→¬→𝜒¬𝜓𝜒	Modus ponens 9243, 9244
9246	→→¬→𝜒¬𝜓𝜒→𝜓→¬→𝜒¬𝜓𝜒	Subs [𝜑↗→¬→𝜒¬𝜓𝜒] into ax-1
9247	→𝜓→¬→𝜒¬𝜓𝜒	Modus ponens 9236, 9246
9248	→→𝜓→¬→𝜒¬𝜓𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗¬→𝜒¬𝜓] into ax-2
9249	→→𝜓¬→𝜒¬𝜓→𝜓𝜒	Modus ponens 9247, 9248
9250	→→→𝜓¬→𝜒¬𝜓→𝜓𝜒→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒	Subs [𝜑↗→→𝜓¬→𝜒¬𝜓→𝜓𝜒, 𝜓↗𝜒] into ax-1
9251	→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒	Modus ponens 9249, 9250
9252	→→𝜒→→𝜓¬→𝜒¬𝜓→𝜓𝜒→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜓¬→𝜒¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
9253	→→𝜒→𝜓¬→𝜒¬𝜓→𝜒→𝜓𝜒	Modus ponens 9251, 9252
9254	→→→𝜒𝜓→𝜒𝜒→𝜓→→𝜒𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜓→𝜒𝜒] into ax-1
9255	→𝜓→→𝜒𝜓→𝜒𝜒	Modus ponens 9160, 9254
9256	→→𝜓→→𝜒𝜓→𝜒𝜒→→𝜓→𝜒𝜓→𝜓→𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗→𝜒𝜓, 𝜒↗→𝜒𝜒] into ax-2
9257	→→𝜓→𝜒𝜓→𝜓→𝜒𝜒	Modus ponens 9255, 9256
9258	→→→𝜓𝜒→𝜓𝜒→¬¬𝜒→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
9259	→¬¬𝜒→→𝜓𝜒→𝜓𝜒	Modus ponens 867, 9258
9260	→→¬¬𝜒→→𝜓𝜒→𝜓𝜒→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→𝜓𝜒] into ax-2
9261	→→¬¬𝜒→𝜓𝜒→¬¬𝜒→𝜓𝜒	Modus ponens 9259, 9260
9262	→→¬¬𝜒→𝜓𝜒→→¬¬𝜒𝜓→¬¬𝜒𝜒	Subs [𝜑↗¬¬𝜒] into ax-2
9263	→→¬¬𝜒𝜓→¬¬𝜒𝜒	Modus ponens 5367, 9262
9264	→→→¬¬𝜒𝜓→¬¬𝜒𝜒→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒	Subs [𝜑↗→→¬¬𝜒𝜓→¬¬𝜒𝜒] into ax-1
9265	→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒	Modus ponens 9263, 9264
9266	→→𝜓→→¬¬𝜒𝜓→¬¬𝜒𝜒→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜓, 𝜒↗→¬¬𝜒𝜒] into ax-2
9267	→→𝜓→¬¬𝜒𝜓→𝜓→¬¬𝜒𝜒	Modus ponens 9265, 9266
9268	→𝜓→¬¬𝜒𝜒	Modus ponens 5375, 9267
9269	→→𝜒¬¬𝜒→¬¬𝜒→𝜒¬¬𝜒	Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜒] into ax-1
9270	→¬¬𝜒→𝜒¬¬𝜒	Modus ponens 9172, 9269
9271	→→¬¬𝜒→𝜒¬¬𝜒→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9272	→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒	Modus ponens 9270, 9271
9273	→→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒	Subs [𝜑↗→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒] into ax-1
9274	→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒	Modus ponens 9272, 9273
9275	→→𝜓→→¬¬𝜒𝜒→¬¬𝜒¬¬𝜒→→𝜓→¬¬𝜒𝜒→𝜓→¬¬𝜒¬¬𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒𝜒, 𝜒↗→¬¬𝜒¬¬𝜒] into ax-2
9276	→→𝜓→¬¬𝜒𝜒→𝜓→¬¬𝜒¬¬𝜒	Modus ponens 9274, 9275
9277	→𝜓→¬¬𝜒¬¬𝜒	Modus ponens 9268, 9276
9278	→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒] into ax-3
9279	→→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒] into ax-1
9280	→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒	Modus ponens 9278, 9279
9281	→→𝜓→→¬¬𝜒¬¬𝜒→¬𝜒¬𝜒→→𝜓→¬¬𝜒¬¬𝜒→𝜓→¬𝜒¬𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬𝜒¬¬𝜒, 𝜒↗→¬𝜒¬𝜒] into ax-2
9282	→→𝜓→¬¬𝜒¬¬𝜒→𝜓→¬𝜒¬𝜒	Modus ponens 9280, 9281
9283	→𝜓→¬𝜒¬𝜒	Modus ponens 9277, 9282
9284	→¬𝜒→𝜓¬𝜒	Subs [𝜑↗¬𝜒] into ax-1
9285	→→¬𝜒→𝜓¬𝜒→¬𝜒→¬𝜒→𝜓¬𝜒	Subs [𝜑↗→¬𝜒→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9286	→¬𝜒→¬𝜒→𝜓¬𝜒	Modus ponens 9284, 9285
9287	→→¬𝜒→¬𝜒→𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
9288	→→¬𝜒¬𝜒→¬𝜒→𝜓¬𝜒	Modus ponens 9286, 9287
9289	→→𝜓→¬𝜒¬𝜒→→𝜓¬𝜒→𝜓¬𝜒	Subs [𝜑↗𝜓, 𝜓↗¬𝜒, 𝜒↗¬𝜒] into ax-2
9290	→→𝜓¬𝜒→𝜓¬𝜒	Modus ponens 9283, 9289
9291	→→→𝜓¬𝜒→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒	Subs [𝜑↗→→𝜓¬𝜒→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9292	→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒	Modus ponens 9290, 9291
9293	→→¬𝜒→→𝜓¬𝜒→𝜓¬𝜒→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗→𝜓¬𝜒] into ax-2
9294	→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬𝜒	Modus ponens 9292, 9293
9295	→→¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9296	→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 5416, 9295
9297	→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9298	→→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
9299	→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Modus ponens 9297, 9298
9300	→→¬¬¬→𝜓¬𝜒→¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗→¬𝜒¬→𝜓¬𝜒] into ax-2
9301	→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Modus ponens 9299, 9300
9302	→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Modus ponens 5419, 9301
9303	→→¬𝜒→¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜓¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
9304	→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Modus ponens 9296, 9303
9305	→→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
9306	→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Modus ponens 9304, 9305
9307	→→¬¬¬→𝜓¬𝜒→→¬𝜒¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗→¬𝜒¬→𝜓¬𝜒, 𝜒↗→¬𝜒¬→𝜓¬𝜒] into ax-2
9308	→→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒	Modus ponens 9306, 9307
9309	→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜓¬𝜒] into ax-1
9310	→→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9311	→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒	Modus ponens 9309, 9310
9312	→→¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬𝜒] into ax-2
9313	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒	Modus ponens 9311, 9312
9314	→→¬¬¬→𝜓¬𝜒→¬𝜒¬→𝜓¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬¬¬→𝜓¬𝜒, 𝜓↗¬𝜒, 𝜒↗¬→𝜓¬𝜒] into ax-2
9315	→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 9302, 9314
9316	→→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9317	→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 9315, 9316
9318	→→¬𝜒→→¬¬¬→𝜓¬𝜒¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬𝜒, 𝜒↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒] into ax-2
9319	→→¬𝜒→¬¬¬→𝜓¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 9317, 9318
9320	→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒	Modus ponens 9309, 9319
9321	→→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
9322	→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 5444, 9321
9323	→→¬𝜒→→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒, 𝜒↗→→𝜓¬𝜒¬¬→𝜓¬𝜒] into ax-2
9324	→→¬𝜒→¬¬¬→𝜓¬𝜒¬→𝜓¬𝜒→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 9322, 9323
9325	→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒	Modus ponens 9320, 9324
9326	→→¬𝜒→→𝜓¬𝜒¬¬→𝜓¬𝜒→→¬𝜒→𝜓¬𝜒→¬𝜒¬¬→𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗¬¬→𝜓¬𝜒] into ax-2
9327	→→¬𝜒→𝜓¬𝜒→¬𝜒¬¬→𝜓¬𝜒	Modus ponens 9325, 9326
9328	→¬𝜒¬¬→𝜓¬𝜒	Modus ponens 9284, 9327
9329	→→¬𝜒¬¬→𝜓¬𝜒→¬→𝜓¬𝜒𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-3
9330	→¬→𝜓¬𝜒𝜒	Modus ponens 9328, 9329
9331	→→¬→𝜓¬𝜒𝜒→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒	Subs [𝜑↗→¬→𝜓¬𝜒𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9332	→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒	Modus ponens 9330, 9331
9333	→→⋀𝜓𝜒→¬→𝜓¬𝜒𝜒→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜓¬𝜒] into ax-2
9334	→→⋀𝜓𝜒¬→𝜓¬𝜒→⋀𝜓𝜒𝜒	Modus ponens 9332, 9333
9335	→→𝜒→𝜑𝜒→⋀𝜓𝜒→𝜒→𝜑𝜒	Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9336	→⋀𝜓𝜒→𝜒→𝜑𝜒	Modus ponens 1834, 9335
9337	→→⋀𝜓𝜒→𝜒→𝜑𝜒→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
9338	→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜑𝜒	Modus ponens 9336, 9337
9339	→⋀𝜓𝜒→𝜑𝜒	Modus ponens 6077, 9338
9340	→→⋀𝜓𝜒→𝜑𝜒→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into ax-2
9341	→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒	Modus ponens 9339, 9340
9342	→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒	Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜑] into ax-1
9343	→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒	Modus ponens 9341, 9342
9344	→→¬¬𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
9345	→→¬¬𝜑→⋀𝜓𝜒𝜑→¬¬𝜑→⋀𝜓𝜒𝜒	Modus ponens 9343, 9344
9346	→¬¬𝜑→⋀𝜓𝜒𝜒	Modus ponens 8934, 9345
9347	→→¬¬𝜑→⋀𝜓𝜒𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-2
9348	→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒	Modus ponens 9346, 9347
9349	→→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒	Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9350	→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒	Modus ponens 9348, 9349
9351	→→⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑𝜒→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑𝜒] into ax-2
9352	→→⋀𝜓𝜒→¬¬𝜑⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜑𝜒	Modus ponens 9350, 9351
9353	→⋀𝜓𝜒→¬¬𝜑𝜒	Modus ponens 8942, 9352
9354	→→𝜒¬¬𝜒→¬¬𝜑→𝜒¬¬𝜒	Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜑] into ax-1
9355	→¬¬𝜑→𝜒¬¬𝜒	Modus ponens 9172, 9354
9356	→→¬¬𝜑→𝜒¬¬𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9357	→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒	Modus ponens 9355, 9356
9358	→→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒	Subs [𝜑↗→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9359	→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒	Modus ponens 9357, 9358
9360	→→⋀𝜓𝜒→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→→⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→¬¬𝜑¬¬𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑𝜒, 𝜒↗→¬¬𝜑¬¬𝜒] into ax-2
9361	→→⋀𝜓𝜒→¬¬𝜑𝜒→⋀𝜓𝜒→¬¬𝜑¬¬𝜒	Modus ponens 9359, 9360
9362	→⋀𝜓𝜒→¬¬𝜑¬¬𝜒	Modus ponens 9353, 9361
9363	→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜒] into ax-3
9364	→→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑, 𝜓↗⋀𝜓𝜒] into ax-1
9365	→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑	Modus ponens 9363, 9364
9366	→→⋀𝜓𝜒→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→→⋀𝜓𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜑¬¬𝜒, 𝜒↗→¬𝜒¬𝜑] into ax-2
9367	→→⋀𝜓𝜒→¬¬𝜑¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜑	Modus ponens 9365, 9366
9368	→⋀𝜓𝜒→¬𝜒¬𝜑	Modus ponens 9362, 9367
9369	→¬𝜒→⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9370	→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒	Subs [𝜑↗→¬𝜒→⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9371	→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒	Modus ponens 9369, 9370
9372	→→¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜒] into ax-2
9373	→→¬𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜒	Modus ponens 9371, 9372
9374	→→⋀𝜓𝜒→¬𝜒¬𝜑→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜑] into ax-2
9375	→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 9368, 9374
9376	→→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9377	→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 9375, 9376
9378	→→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜑→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2
9379	→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 9377, 9378
9380	→¬𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 9369, 9379
9381	→→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9382	→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 8976, 9381
9383	→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9384	→→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
9385	→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Modus ponens 9383, 9384
9386	→→¬¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜑] into ax-2
9387	→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Modus ponens 9385, 9386
9388	→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Modus ponens 8979, 9387
9389	→→¬𝜒→¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9390	→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Modus ponens 9382, 9389
9391	→→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
9392	→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Modus ponens 9390, 9391
9393	→→¬¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗→¬𝜒¬→⋀𝜓𝜒¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜑] into ax-2
9394	→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑	Modus ponens 9392, 9393
9395	→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜑] into ax-1
9396	→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1
9397	→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒	Modus ponens 9395, 9396
9398	→→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒] into ax-2
9399	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒	Modus ponens 9397, 9398
9400	→→¬¬¬→⋀𝜓𝜒¬𝜑→¬𝜒¬→⋀𝜓𝜒¬𝜑→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9401	→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 9388, 9400
9402	→→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9403	→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 9401, 9402
9404	→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑] into ax-2
9405	→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 9403, 9404
9406	→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑	Modus ponens 9395, 9405
9407	→→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑, 𝜓↗¬𝜒] into ax-1
9408	→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9004, 9407
9409	→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9410	→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜑¬→⋀𝜓𝜒¬𝜑→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9408, 9409
9411	→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9406, 9410
9412	→→¬𝜒→→⋀𝜓𝜒¬𝜑¬¬→⋀𝜓𝜒¬𝜑→→¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒¬¬→⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑, 𝜒↗¬¬→⋀𝜓𝜒¬𝜑] into ax-2
9413	→→¬𝜒→⋀𝜓𝜒¬𝜑→¬𝜒¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9411, 9412
9414	→¬𝜒¬¬→⋀𝜓𝜒¬𝜑	Modus ponens 9380, 9413
9415	→→¬𝜒¬¬→⋀𝜓𝜒¬𝜑→¬→⋀𝜓𝜒¬𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-3
9416	→¬→⋀𝜓𝜒¬𝜑𝜒	Modus ponens 9414, 9415
9417	→→¬→⋀𝜓𝜒¬𝜑𝜒→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜒, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-1
9418	→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒	Modus ponens 9416, 9417
9419	→→⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜑, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9420	→→⋀⋀𝜓𝜒𝜑¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒	Modus ponens 9418, 9419
9421	→⋀⋀𝜓𝜒𝜑𝜒	Modus ponens 9016, 9420
9422	→→⋀⋀𝜓𝜒𝜑𝜒→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒	Subs [𝜑↗→⋀⋀𝜓𝜒𝜑𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-1
9423	→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒	Modus ponens 9421, 9422
9424	→→¬→⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜑𝜒→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜑] into ax-2
9425	→→¬→⋀𝜓𝜒¬𝜑⋀⋀𝜓𝜒𝜑→¬→⋀𝜓𝜒¬𝜑𝜒	Modus ponens 9423, 9424
9426	→→¬→⋀𝜓𝜒¬𝜑𝜒→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜑𝜒, 𝜓↗𝜑] into ax-1
9427	→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒	Modus ponens 9416, 9426
9428	→→𝜑→¬→⋀𝜓𝜒¬𝜑𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒	Subs [𝜓↗¬→⋀𝜓𝜒¬𝜑] into ax-2
9429	→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒	Modus ponens 9427, 9428
9430	→→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒	Subs [𝜑↗→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9431	→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒	Modus ponens 9429, 9430
9432	→→⋀𝜓𝜒→→𝜑¬→⋀𝜓𝜒¬𝜑→𝜑𝜒→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜑¬→⋀𝜓𝜒¬𝜑, 𝜒↗→𝜑𝜒] into ax-2
9433	→→⋀𝜓𝜒→𝜑¬→⋀𝜓𝜒¬𝜑→⋀𝜓𝜒→𝜑𝜒	Modus ponens 9431, 9432
9434	→→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒	Subs [𝜑↗→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
9435	→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒	Modus ponens 9341, 9434
9436	→→𝜑→→⋀𝜓𝜒𝜑→⋀𝜓𝜒𝜒→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜒	Subs [𝜓↗→⋀𝜓𝜒𝜑, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
9437	→→𝜑→⋀𝜓𝜒𝜑→𝜑→⋀𝜓𝜒𝜒	Modus ponens 9435, 9436
9438	→→→𝜑⋀𝜓𝜒→𝜑𝜒→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9439	→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒	Modus ponens 6081, 9438
9440	→→¬¬⋀𝜓𝜒→→𝜑⋀𝜓𝜒→𝜑𝜒→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
9441	→→¬¬⋀𝜓𝜒→𝜑⋀𝜓𝜒→¬¬⋀𝜓𝜒→𝜑𝜒	Modus ponens 9439, 9440
9442	→¬¬⋀𝜓𝜒→𝜑𝜒	Modus ponens 5479, 9441
9443	→→¬¬⋀𝜓𝜒→𝜑𝜒→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-2
9444	→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒	Modus ponens 9442, 9443
9445	→→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒	Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
9446	→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒	Modus ponens 9444, 9445
9447	→→𝜑→→¬¬⋀𝜓𝜒𝜑→¬¬⋀𝜓𝜒𝜒→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜒	Subs [𝜓↗→¬¬⋀𝜓𝜒𝜑, 𝜒↗→¬¬⋀𝜓𝜒𝜒] into ax-2
9448	→→𝜑→¬¬⋀𝜓𝜒𝜑→𝜑→¬¬⋀𝜓𝜒𝜒	Modus ponens 9446, 9447
9449	→𝜑→¬¬⋀𝜓𝜒𝜒	Modus ponens 5487, 9448
9450	→→𝜒¬¬𝜒→¬¬⋀𝜓𝜒→𝜒¬¬𝜒	Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜓𝜒] into ax-1
9451	→¬¬⋀𝜓𝜒→𝜒¬¬𝜒	Modus ponens 9172, 9450
9452	→→¬¬⋀𝜓𝜒→𝜒¬¬𝜒→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒	Subs [𝜑↗¬¬⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
9453	→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒	Modus ponens 9451, 9452
9454	→→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒	Subs [𝜑↗→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒, 𝜓↗𝜑] into ax-1
9455	→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒	Modus ponens 9453, 9454
9456	→→𝜑→→¬¬⋀𝜓𝜒𝜒→¬¬⋀𝜓𝜒¬¬𝜒→→𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→¬¬⋀𝜓𝜒¬¬𝜒	Subs [𝜓↗→¬¬⋀𝜓𝜒𝜒, 𝜒↗→¬¬⋀𝜓𝜒¬¬𝜒] into ax-2
9457	→→𝜑→¬¬⋀𝜓𝜒𝜒→𝜑→¬¬⋀𝜓𝜒¬¬𝜒	Modus ponens 9455, 9456
9458	→𝜑→¬¬⋀𝜓𝜒¬¬𝜒	Modus ponens 9449, 9457
9459	→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-3
9460	→→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
9461	→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒	Modus ponens 9459, 9460
9462	→→𝜑→→¬¬⋀𝜓𝜒¬¬𝜒→¬𝜒¬⋀𝜓𝜒→→𝜑→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→¬𝜒¬⋀𝜓𝜒	Subs [𝜓↗→¬¬⋀𝜓𝜒¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜓𝜒] into ax-2
9463	→→𝜑→¬¬⋀𝜓𝜒¬¬𝜒→𝜑→¬𝜒¬⋀𝜓𝜒	Modus ponens 9461, 9462
9464	→𝜑→¬𝜒¬⋀𝜓𝜒	Modus ponens 9458, 9463
9465	→¬𝜒→𝜑¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗𝜑] into ax-1
9466	→→¬𝜒→𝜑¬𝜒→¬𝜒→¬𝜒→𝜑¬𝜒	Subs [𝜑↗→¬𝜒→𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1
9467	→¬𝜒→¬𝜒→𝜑¬𝜒	Modus ponens 9465, 9466
9468	→→¬𝜒→¬𝜒→𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→𝜑¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→𝜑¬𝜒] into ax-2
9469	→→¬𝜒¬𝜒→¬𝜒→𝜑¬𝜒	Modus ponens 9467, 9468
9470	→→𝜑→¬𝜒¬⋀𝜓𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜓↗¬𝜒, 𝜒↗¬⋀𝜓𝜒] into ax-2
9471	→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 9464, 9470
9472	→→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9473	→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 9471, 9472
9474	→→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓𝜒→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
9475	→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 9473, 9474
9476	→¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 9465, 9475
9477	→→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9478	→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5528, 9477
9479	→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9480	→→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9481	→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9479, 9480
9482	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9483	→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9481, 9482
9484	→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 5531, 9483
9485	→→¬𝜒→¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9486	→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9478, 9485
9487	→→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9488	→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9486, 9487
9489	→→¬¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗→¬𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9490	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9488, 9489
9491	→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓𝜒] into ax-1
9492	→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
9493	→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒	Modus ponens 9491, 9492
9494	→→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒] into ax-2
9495	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒	Modus ponens 9493, 9494
9496	→→¬¬¬→𝜑¬⋀𝜓𝜒→¬𝜒¬→𝜑¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9497	→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9484, 9496
9498	→→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9499	→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9497, 9498
9500	→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒] into ax-2
9501	→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9499, 9500
9502	→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒	Modus ponens 9491, 9501
9503	→→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒, 𝜓↗¬𝜒] into ax-1
9504	→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 5556, 9503
9505	→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9506	→→¬𝜒→¬¬¬→𝜑¬⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9504, 9505
9507	→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9502, 9506
9508	→→¬𝜒→→𝜑¬⋀𝜓𝜒¬¬→𝜑¬⋀𝜓𝜒→→¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒¬¬→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗¬¬→𝜑¬⋀𝜓𝜒] into ax-2
9509	→→¬𝜒→𝜑¬⋀𝜓𝜒→¬𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9507, 9508
9510	→¬𝜒¬¬→𝜑¬⋀𝜓𝜒	Modus ponens 9476, 9509
9511	→→¬𝜒¬¬→𝜑¬⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-3
9512	→¬→𝜑¬⋀𝜓𝜒𝜒	Modus ponens 9510, 9511
9513	→→¬→𝜑¬⋀𝜓𝜒𝜒→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
9514	→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒	Modus ponens 9512, 9513
9515	→→⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-2
9516	→→⋀𝜑⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 9514, 9515
9517	→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 5568, 9516	simprr
9518	→𝜑→𝜃𝜑	Subs [𝜓↗𝜃] into ax-1
9519	→→𝜑→𝜃𝜑→⋀𝜑𝜓→𝜑→𝜃𝜑	Subs [𝜑↗→𝜑→𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9520	→⋀𝜑𝜓→𝜑→𝜃𝜑	Modus ponens 9518, 9519
9521	→→⋀𝜑𝜓→𝜑→𝜃𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜃𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗→𝜃𝜑] into ax-2
9522	→→⋀𝜑𝜓𝜑→⋀𝜑𝜓→𝜃𝜑	Modus ponens 9520, 9521
9523	→⋀𝜑𝜓→𝜃𝜑	Modus ponens simpl, 9522
9524	↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into df-an
9525	→¬¬𝜃𝜃	Subs [𝜑↗𝜃] into notnotr
9526	→𝜃→⋀𝜑𝜓𝜃	Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓] into ax-1
9527	→→𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃	Subs [𝜑↗→𝜃→⋀𝜑𝜓𝜃, 𝜓↗¬¬𝜃] into ax-1
9528	→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃	Modus ponens 9526, 9527
9529	→→¬¬𝜃→𝜃→⋀𝜑𝜓𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑𝜓𝜃	Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑𝜓𝜃] into ax-2
9530	→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑𝜓𝜃	Modus ponens 9528, 9529
9531	→¬¬𝜃→⋀𝜑𝜓𝜃	Modus ponens 9525, 9530
9532	→→⋀𝜑𝜓→𝜃𝜑→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃, 𝜒↗𝜑] into ax-2
9533	→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑	Modus ponens 9523, 9532
9534	→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑	Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑, 𝜓↗¬¬𝜃] into ax-1
9535	→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑	Modus ponens 9533, 9534
9536	→→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜑	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
9537	→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜑	Modus ponens 9535, 9536
9538	→¬¬𝜃→⋀𝜑𝜓𝜑	Modus ponens 9531, 9537
9539	→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬𝜃] into ax-1
9540	→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9541	→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓	Modus ponens 9539, 9540
9542	→→⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→¬¬𝜃⋀𝜑𝜓] into ax-2
9543	→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓	Modus ponens 9541, 9542
9544	→→¬¬𝜃→⋀𝜑𝜓𝜑→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
9545	→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑	Modus ponens 9538, 9544
9546	→→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑	Subs [𝜑↗→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9547	→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑	Modus ponens 9545, 9546
9548	→→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜑→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃⋀𝜑𝜓, 𝜒↗→¬¬𝜃𝜑] into ax-2
9549	→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜑	Modus ponens 9547, 9548
9550	→⋀𝜑𝜓→¬¬𝜃𝜑	Modus ponens 9539, 9549
9551	→→𝜑¬¬𝜑→¬¬𝜃→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜃] into ax-1
9552	→¬¬𝜃→𝜑¬¬𝜑	Modus ponens notnot, 9551
9553	→→¬¬𝜃→𝜑¬¬𝜑→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑	Subs [𝜑↗¬¬𝜃, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
9554	→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑	Modus ponens 9552, 9553
9555	→→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑	Subs [𝜑↗→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9556	→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑	Modus ponens 9554, 9555
9557	→→⋀𝜑𝜓→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→→⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→¬¬𝜃¬¬𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃𝜑, 𝜒↗→¬¬𝜃¬¬𝜑] into ax-2
9558	→→⋀𝜑𝜓→¬¬𝜃𝜑→⋀𝜑𝜓→¬¬𝜃¬¬𝜑	Modus ponens 9556, 9557
9559	→⋀𝜑𝜓→¬¬𝜃¬¬𝜑	Modus ponens 9550, 9558
9560	→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜑] into ax-3
9561	→→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃, 𝜓↗⋀𝜑𝜓] into ax-1
9562	→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃	Modus ponens 9560, 9561
9563	→→⋀𝜑𝜓→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→→⋀𝜑𝜓→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜃	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃¬¬𝜑, 𝜒↗→¬𝜑¬𝜃] into ax-2
9564	→→⋀𝜑𝜓→¬¬𝜃¬¬𝜑→⋀𝜑𝜓→¬𝜑¬𝜃	Modus ponens 9562, 9563
9565	→⋀𝜑𝜓→¬𝜑¬𝜃	Modus ponens 9559, 9564
9566	→→⋀𝜑𝜓→¬𝜑¬𝜃→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜑, 𝜒↗¬𝜃] into ax-2
9567	→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃	Modus ponens 9565, 9566
9568	→→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9569	→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃	Modus ponens 9567, 9568
9570	→→¬𝜑→→⋀𝜑𝜓¬𝜑→⋀𝜑𝜓¬𝜃→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜑, 𝜒↗→⋀𝜑𝜓¬𝜃] into ax-2
9571	→→¬𝜑→⋀𝜑𝜓¬𝜑→¬𝜑→⋀𝜑𝜓¬𝜃	Modus ponens 9569, 9570
9572	→¬𝜑→⋀𝜑𝜓¬𝜃	Modus ponens 8680, 9571
9573	→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃] into id
9574	→→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9575	→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9573, 9574
9576	→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃] into notnotr
9577	→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9578	→→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9579	→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Modus ponens 9577, 9578
9580	→→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜃] into ax-2
9581	→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Modus ponens 9579, 9580
9582	→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Modus ponens 9576, 9581
9583	→→¬𝜑→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9584	→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Modus ponens 9575, 9583
9585	→→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9586	→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Modus ponens 9584, 9585
9587	→→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→¬𝜑¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜑¬→⋀𝜑𝜓¬𝜃] into ax-2
9588	→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃	Modus ponens 9586, 9587
9589	→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9590	→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1
9591	→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑	Modus ponens 9589, 9590
9592	→→¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑] into ax-2
9593	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑	Modus ponens 9591, 9592
9594	→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜑¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9595	→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9582, 9594
9596	→→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9597	→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9595, 9596
9598	→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃] into ax-2
9599	→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9597, 9598
9600	→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9589, 9599
9601	→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→⋀𝜑𝜓¬𝜃] into ax-3
9602	→→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜑] into ax-1
9603	→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9601, 9602
9604	→→¬𝜑→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9605	→→¬𝜑→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9603, 9604
9606	→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9600, 9605
9607	→→¬𝜑→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑¬¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜃, 𝜒↗¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9608	→→¬𝜑→⋀𝜑𝜓¬𝜃→¬𝜑¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9606, 9607
9609	→¬𝜑¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9572, 9608
9610	→→¬𝜑¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃𝜑	Subs [𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-3
9611	→¬→⋀𝜑𝜓¬𝜃𝜑	Modus ponens 9609, 9610
9612	→↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into biimp
9613	→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9524, 9612
9614	→→¬→⋀𝜑𝜓¬𝜃𝜑→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜃] into ax-1
9615	→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑	Modus ponens 9611, 9614
9616	→→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜑] into ax-2
9617	→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑	Modus ponens 9615, 9616
9618	→⋀⋀𝜑𝜓𝜃𝜑	Modus ponens 9613, 9617
9619	→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into simpl
9620	→↔⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃	Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into bicom1
9621	↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃	Modus ponens 9524, 9620
9622	→↔¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃] into biimp
9623	→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃	Modus ponens 9621, 9622
9624	→→⋀⋀𝜑𝜓𝜃𝜑→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑	Subs [𝜑↗→⋀⋀𝜑𝜓𝜃𝜑, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-1
9625	→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑	Modus ponens 9618, 9624
9626	→→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜑→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃, 𝜒↗𝜑] into ax-2
9627	→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜑	Modus ponens 9625, 9626
9628	→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into pm3.2im
9629	→→¬→⋀𝜑𝜓¬𝜃𝜑→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜑, 𝜓↗𝜃] into ax-1
9630	→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑	Modus ponens 9611, 9629
9631	→→𝜃→¬→⋀𝜑𝜓¬𝜃𝜑→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑	Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜑] into ax-2
9632	→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑	Modus ponens 9630, 9631
9633	→→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑	Subs [𝜑↗→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑, 𝜓↗⋀𝜑𝜓] into ax-1
9634	→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑	Modus ponens 9632, 9633
9635	→→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜑→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜑	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→𝜃𝜑] into ax-2
9636	→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜑	Modus ponens 9634, 9635
9637	→𝜃𝜃	Subs [𝜑↗𝜃] into id
9638	→→𝜃→⋀𝜑𝜓𝜃→𝜃→𝜃→⋀𝜑𝜓𝜃	Subs [𝜑↗→𝜃→⋀𝜑𝜓𝜃, 𝜓↗𝜃] into ax-1
9639	→𝜃→𝜃→⋀𝜑𝜓𝜃	Modus ponens 9526, 9638
9640	→→𝜃→𝜃→⋀𝜑𝜓𝜃→→𝜃𝜃→𝜃→⋀𝜑𝜓𝜃	Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑𝜓𝜃] into ax-2
9641	→→𝜃𝜃→𝜃→⋀𝜑𝜓𝜃	Modus ponens 9639, 9640
9642	→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑	Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑, 𝜓↗𝜃] into ax-1
9643	→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑	Modus ponens 9533, 9642
9644	→→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜑→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜑	Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
9645	→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜑	Modus ponens 9643, 9644
9646	→𝜃→⋀𝜑𝜓𝜑	Modus ponens 9526, 9645
9647	→⋀𝜑𝜓→𝜃⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃] into ax-1
9648	→→⋀𝜑𝜓→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓	Subs [𝜑↗→⋀𝜑𝜓→𝜃⋀𝜑𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9649	→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓	Modus ponens 9647, 9648
9650	→→⋀⋀𝜑𝜓𝜒→⋀𝜑𝜓→𝜃⋀𝜑𝜓→→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜃⋀𝜑𝜓] into ax-2
9651	→→⋀⋀𝜑𝜓𝜒⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓	Modus ponens 9649, 9650
9652	→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓	Modus ponens 9619, 9651
9653	→→𝜃→⋀𝜑𝜓𝜑→→𝜃⋀𝜑𝜓→𝜃𝜑	Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜑] into ax-2
9654	→→𝜃⋀𝜑𝜓→𝜃𝜑	Modus ponens 9646, 9653
9655	→→→𝜃⋀𝜑𝜓→𝜃𝜑→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑	Subs [𝜑↗→→𝜃⋀𝜑𝜓→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9656	→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑	Modus ponens 9654, 9655
9657	→→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜑→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀𝜑𝜓, 𝜒↗→𝜃𝜑] into ax-2
9658	→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜑	Modus ponens 9656, 9657
9659	→⋀⋀𝜑𝜓𝜒→𝜃𝜑	Modus ponens 9652, 9658
9660	→𝜃→⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9661	→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗→𝜃→⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1
9662	→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 9660, 9661
9663	→→𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜃] into ax-2
9664	→→𝜃𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 9662, 9663
9665	→→⋀⋀𝜑𝜓𝜒→𝜃𝜑→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜑] into ax-2
9666	→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 9659, 9665
9667	→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗𝜃] into ax-1
9668	→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 9666, 9667
9669	→→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
9670	→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 9668, 9669
9671	→𝜃→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 9660, 9670
9672	→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into ax-1
9673	→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9674	→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒	Modus ponens 9672, 9673
9675	→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃⋀⋀𝜑𝜓𝜒] into ax-2
9676	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒	Modus ponens 9674, 9675
9677	→→𝜃→⋀⋀𝜑𝜓𝜒𝜑→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑	Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
9678	→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑	Modus ponens 9671, 9677
9679	→→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑	Subs [𝜑↗→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9680	→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑	Modus ponens 9678, 9679
9681	→→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜑→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜑] into ax-2
9682	→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜑	Modus ponens 9680, 9681
9683	↔⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into df-an
9684	→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗→𝜃→⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1
9685	→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 9660, 9684
9686	→→¬¬𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜃] into ax-2
9687	→→¬¬𝜃𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 9685, 9686
9688	→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 9525, 9687
9689	→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗¬¬𝜃] into ax-1
9690	→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 9666, 9689
9691	→→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
9692	→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 9690, 9691
9693	→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 9688, 9692
9694	→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1
9695	→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9696	→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒	Modus ponens 9694, 9695
9697	→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃⋀⋀𝜑𝜓𝜒] into ax-2
9698	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒	Modus ponens 9696, 9697
9699	→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
9700	→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑	Modus ponens 9693, 9699
9701	→→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑	Subs [𝜑↗→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9702	→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑	Modus ponens 9700, 9701
9703	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃𝜑] into ax-2
9704	→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑	Modus ponens 9702, 9703
9705	→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑	Modus ponens 9694, 9704
9706	→→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑	Subs [𝜑↗→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9707	→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑	Modus ponens 9554, 9706
9708	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜑→¬¬𝜃¬¬𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃𝜑, 𝜒↗→¬¬𝜃¬¬𝜑] into ax-2
9709	→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑	Modus ponens 9707, 9708
9710	→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑	Modus ponens 9705, 9709
9711	→→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9712	→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃	Modus ponens 9560, 9711
9713	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜑→¬𝜑¬𝜃→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜑, 𝜒↗→¬𝜑¬𝜃] into ax-2
9714	→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃	Modus ponens 9712, 9713
9715	→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃	Modus ponens 9710, 9714
9716	→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9717	→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜓↗¬𝜑] into ax-1
9718	→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑	Modus ponens 9716, 9717
9719	→→¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜑] into ax-2
9720	→→¬𝜑¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑	Modus ponens 9718, 9719
9721	→→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬𝜃] into ax-2
9722	→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9715, 9721
9723	→→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9724	→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9722, 9723
9725	→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9726	→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9724, 9725
9727	→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9716, 9726
9728	→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into id
9729	→→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9730	→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9728, 9729
9731	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into notnotr
9732	→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9733	→→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9734	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9732, 9733
9735	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9736	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9734, 9735
9737	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9731, 9736
9738	→→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9739	→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9730, 9738
9740	→→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9741	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9739, 9740
9742	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9743	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9741, 9742
9744	→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9745	→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1
9746	→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑	Modus ponens 9744, 9745
9747	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑] into ax-2
9748	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑	Modus ponens 9746, 9747
9749	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9750	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9737, 9749
9751	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9752	→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9750, 9751
9753	→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9754	→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9752, 9753
9755	→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9744, 9754
9756	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3
9757	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜑] into ax-1
9758	→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9756, 9757
9759	→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9760	→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9758, 9759
9761	→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9755, 9760
9762	→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9763	→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9761, 9762
9764	→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9727, 9763
9765	→→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑	Subs [𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3
9766	→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑	Modus ponens 9764, 9765
9767	→↔⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into biimp
9768	→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9683, 9767
9769	→→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
9770	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑	Modus ponens 9766, 9769
9771	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗𝜑] into ax-2
9772	→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 9770, 9771
9773	→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 9768, 9772	simplll
9774	→𝜓→𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜃] into ax-1
9775	→→𝜓→𝜃𝜓→⋀𝜑𝜓→𝜓→𝜃𝜓	Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9776	→⋀𝜑𝜓→𝜓→𝜃𝜓	Modus ponens 9774, 9775
9777	→→⋀𝜑𝜓→𝜓→𝜃𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜃𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜃𝜓] into ax-2
9778	→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜃𝜓	Modus ponens 9776, 9777
9779	→⋀𝜑𝜓→𝜃𝜓	Modus ponens simpr, 9778
9780	→→⋀𝜑𝜓→𝜃𝜓→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
9781	→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓	Modus ponens 9779, 9780
9782	→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓	Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓, 𝜓↗¬¬𝜃] into ax-1
9783	→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓	Modus ponens 9781, 9782
9784	→→¬¬𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
9785	→→¬¬𝜃→⋀𝜑𝜓𝜃→¬¬𝜃→⋀𝜑𝜓𝜓	Modus ponens 9783, 9784
9786	→¬¬𝜃→⋀𝜑𝜓𝜓	Modus ponens 9531, 9785
9787	→→¬¬𝜃→⋀𝜑𝜓𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
9788	→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓	Modus ponens 9786, 9787
9789	→→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓	Subs [𝜑↗→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9790	→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓	Modus ponens 9788, 9789
9791	→→⋀𝜑𝜓→→¬¬𝜃⋀𝜑𝜓→¬¬𝜃𝜓→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃⋀𝜑𝜓, 𝜒↗→¬¬𝜃𝜓] into ax-2
9792	→→⋀𝜑𝜓→¬¬𝜃⋀𝜑𝜓→⋀𝜑𝜓→¬¬𝜃𝜓	Modus ponens 9790, 9791
9793	→⋀𝜑𝜓→¬¬𝜃𝜓	Modus ponens 9539, 9792
9794	→→𝜓¬¬𝜓→¬¬𝜃→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜃] into ax-1
9795	→¬¬𝜃→𝜓¬¬𝜓	Modus ponens 448, 9794
9796	→→¬¬𝜃→𝜓¬¬𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Subs [𝜑↗¬¬𝜃, 𝜒↗¬¬𝜓] into ax-2
9797	→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Modus ponens 9795, 9796
9798	→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9799	→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Modus ponens 9797, 9798
9800	→→⋀𝜑𝜓→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→¬¬𝜃¬¬𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
9801	→→⋀𝜑𝜓→¬¬𝜃𝜓→⋀𝜑𝜓→¬¬𝜃¬¬𝜓	Modus ponens 9799, 9800
9802	→⋀𝜑𝜓→¬¬𝜃¬¬𝜓	Modus ponens 9793, 9801
9803	→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜓] into ax-3
9804	→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜑𝜓] into ax-1
9805	→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Modus ponens 9803, 9804
9806	→→⋀𝜑𝜓→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜑𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜃	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
9807	→→⋀𝜑𝜓→¬¬𝜃¬¬𝜓→⋀𝜑𝜓→¬𝜓¬𝜃	Modus ponens 9805, 9806
9808	→⋀𝜑𝜓→¬𝜓¬𝜃	Modus ponens 9802, 9807
9809	→→⋀𝜑𝜓→¬𝜓¬𝜃→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
9810	→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃	Modus ponens 9808, 9809
9811	→→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9812	→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃	Modus ponens 9810, 9811
9813	→→¬𝜓→→⋀𝜑𝜓¬𝜓→⋀𝜑𝜓¬𝜃→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜓, 𝜒↗→⋀𝜑𝜓¬𝜃] into ax-2
9814	→→¬𝜓→⋀𝜑𝜓¬𝜓→¬𝜓→⋀𝜑𝜓¬𝜃	Modus ponens 9812, 9813
9815	→¬𝜓→⋀𝜑𝜓¬𝜃	Modus ponens 8871, 9814
9816	→→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9817	→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9573, 9816
9818	→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9819	→→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9820	→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Modus ponens 9818, 9819
9821	→→¬¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜃] into ax-2
9822	→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Modus ponens 9820, 9821
9823	→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Modus ponens 9576, 9822
9824	→→¬𝜓→¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9825	→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Modus ponens 9817, 9824
9826	→→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9827	→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Modus ponens 9825, 9826
9828	→→¬¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜑𝜓¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑𝜓¬𝜃] into ax-2
9829	→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃	Modus ponens 9827, 9828
9830	→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑𝜓¬𝜃] into ax-1
9831	→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
9832	→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓	Modus ponens 9830, 9831
9833	→→¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓] into ax-2
9834	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓	Modus ponens 9832, 9833
9835	→→¬¬¬→⋀𝜑𝜓¬𝜃→¬𝜓¬→⋀𝜑𝜓¬𝜃→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑𝜓¬𝜃] into ax-2
9836	→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9823, 9835
9837	→→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9838	→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9836, 9837
9839	→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃] into ax-2
9840	→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9838, 9839
9841	→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃	Modus ponens 9830, 9840
9842	→→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃, 𝜓↗¬𝜓] into ax-1
9843	→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9601, 9842
9844	→→¬𝜓→→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9845	→→¬𝜓→¬¬¬→⋀𝜑𝜓¬𝜃¬→⋀𝜑𝜓¬𝜃→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9843, 9844
9846	→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9841, 9845
9847	→→¬𝜓→→⋀𝜑𝜓¬𝜃¬¬→⋀𝜑𝜓¬𝜃→→¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓¬¬→⋀𝜑𝜓¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑𝜓¬𝜃, 𝜒↗¬¬→⋀𝜑𝜓¬𝜃] into ax-2
9848	→→¬𝜓→⋀𝜑𝜓¬𝜃→¬𝜓¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9846, 9847
9849	→¬𝜓¬¬→⋀𝜑𝜓¬𝜃	Modus ponens 9815, 9848
9850	→→¬𝜓¬¬→⋀𝜑𝜓¬𝜃→¬→⋀𝜑𝜓¬𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-3
9851	→¬→⋀𝜑𝜓¬𝜃𝜓	Modus ponens 9849, 9850
9852	→→¬→⋀𝜑𝜓¬𝜃𝜓→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜃] into ax-1
9853	→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓	Modus ponens 9851, 9852
9854	→→⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜓] into ax-2
9855	→→⋀⋀𝜑𝜓𝜃¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓	Modus ponens 9853, 9854
9856	→⋀⋀𝜑𝜓𝜃𝜓	Modus ponens 9613, 9855
9857	→→⋀⋀𝜑𝜓𝜃𝜓→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓	Subs [𝜑↗→⋀⋀𝜑𝜓𝜃𝜓, 𝜓↗¬→⋀𝜑𝜓¬𝜃] into ax-1
9858	→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓	Modus ponens 9856, 9857
9859	→→¬→⋀𝜑𝜓¬𝜃→⋀⋀𝜑𝜓𝜃𝜓→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓	Subs [𝜑↗¬→⋀𝜑𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜃, 𝜒↗𝜓] into ax-2
9860	→→¬→⋀𝜑𝜓¬𝜃⋀⋀𝜑𝜓𝜃→¬→⋀𝜑𝜓¬𝜃𝜓	Modus ponens 9858, 9859
9861	→→¬→⋀𝜑𝜓¬𝜃𝜓→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓	Subs [𝜑↗→¬→⋀𝜑𝜓¬𝜃𝜓, 𝜓↗𝜃] into ax-1
9862	→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓	Modus ponens 9851, 9861
9863	→→𝜃→¬→⋀𝜑𝜓¬𝜃𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓	Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜑𝜓¬𝜃, 𝜒↗𝜓] into ax-2
9864	→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓	Modus ponens 9862, 9863
9865	→→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓	Subs [𝜑↗→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
9866	→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓	Modus ponens 9864, 9865
9867	→→⋀𝜑𝜓→→𝜃¬→⋀𝜑𝜓¬𝜃→𝜃𝜓→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜃¬→⋀𝜑𝜓¬𝜃, 𝜒↗→𝜃𝜓] into ax-2
9868	→→⋀𝜑𝜓→𝜃¬→⋀𝜑𝜓¬𝜃→⋀𝜑𝜓→𝜃𝜓	Modus ponens 9866, 9867
9869	→→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓	Subs [𝜑↗→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓, 𝜓↗𝜃] into ax-1
9870	→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓	Modus ponens 9781, 9869
9871	→→𝜃→→⋀𝜑𝜓𝜃→⋀𝜑𝜓𝜓→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜓	Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑𝜓𝜃, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
9872	→→𝜃→⋀𝜑𝜓𝜃→𝜃→⋀𝜑𝜓𝜓	Modus ponens 9870, 9871
9873	→𝜃→⋀𝜑𝜓𝜓	Modus ponens 9526, 9872
9874	→→𝜃→⋀𝜑𝜓𝜓→→𝜃⋀𝜑𝜓→𝜃𝜓	Subs [𝜑↗𝜃, 𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
9875	→→𝜃⋀𝜑𝜓→𝜃𝜓	Modus ponens 9873, 9874
9876	→→→𝜃⋀𝜑𝜓→𝜃𝜓→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓	Subs [𝜑↗→→𝜃⋀𝜑𝜓→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9877	→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓	Modus ponens 9875, 9876
9878	→→⋀⋀𝜑𝜓𝜒→→𝜃⋀𝜑𝜓→𝜃𝜓→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀𝜑𝜓, 𝜒↗→𝜃𝜓] into ax-2
9879	→→⋀⋀𝜑𝜓𝜒→𝜃⋀𝜑𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓	Modus ponens 9877, 9878
9880	→⋀⋀𝜑𝜓𝜒→𝜃𝜓	Modus ponens 9652, 9879
9881	→→⋀⋀𝜑𝜓𝜒→𝜃𝜓→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
9882	→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 9880, 9881
9883	→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1
9884	→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 9882, 9883
9885	→→𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
9886	→→𝜃→⋀⋀𝜑𝜓𝜒𝜃→𝜃→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 9884, 9885
9887	→𝜃→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 9660, 9886
9888	→→𝜃→⋀⋀𝜑𝜓𝜒𝜓→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓	Subs [𝜑↗𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
9889	→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓	Modus ponens 9887, 9888
9890	→→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓	Subs [𝜑↗→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9891	→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓	Modus ponens 9889, 9890
9892	→→⋀⋀𝜑𝜓𝜒→→𝜃⋀⋀𝜑𝜓𝜒→𝜃𝜓→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
9893	→→⋀⋀𝜑𝜓𝜒→𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→𝜃𝜓	Modus ponens 9891, 9892
9894	→→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1
9895	→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 9882, 9894
9896	→→¬¬𝜃→→⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
9897	→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 9895, 9896
9898	→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 9688, 9897
9899	→→¬¬𝜃→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
9900	→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9898, 9899
9901	→→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9902	→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9900, 9901
9903	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2
9904	→→⋀⋀𝜑𝜓𝜒→¬¬𝜃⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9902, 9903
9905	→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9694, 9904
9906	→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9907	→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Modus ponens 9797, 9906
9908	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
9909	→→⋀⋀𝜑𝜓𝜒→¬¬𝜃𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓	Modus ponens 9907, 9908
9910	→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓	Modus ponens 9905, 9909
9911	→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9912	→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Modus ponens 9803, 9911
9913	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
9914	→→⋀⋀𝜑𝜓𝜒→¬¬𝜃¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃	Modus ponens 9912, 9913
9915	→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃	Modus ponens 9910, 9914
9916	→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
9917	→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
9918	→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓	Modus ponens 9916, 9917
9919	→→¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜓] into ax-2
9920	→→¬𝜓¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓	Modus ponens 9918, 9919
9921	→→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
9922	→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9915, 9921
9923	→→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9924	→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9922, 9923
9925	→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9926	→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9924, 9925
9927	→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9916, 9926
9928	→→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9929	→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9728, 9928
9930	→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9931	→→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9932	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9930, 9931
9933	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9934	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9932, 9933
9935	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9731, 9934
9936	→→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9937	→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9929, 9936
9938	→→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9939	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9937, 9938
9940	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9941	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9939, 9940
9942	→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-1
9943	→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
9944	→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓	Modus ponens 9942, 9943
9945	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓] into ax-2
9946	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓	Modus ponens 9944, 9945
9947	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9948	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9935, 9947
9949	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9950	→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9948, 9949
9951	→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9952	→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9950, 9951
9953	→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9942, 9952
9954	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
9955	→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9756, 9954
9956	→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9957	→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9955, 9956
9958	→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9953, 9957
9959	→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜃¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-2
9960	→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜃→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9958, 9959
9961	→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃	Modus ponens 9927, 9960
9962	→→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃] into ax-3
9963	→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓	Modus ponens 9961, 9962
9964	→→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
9965	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓	Modus ponens 9963, 9964
9966	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬→⋀⋀𝜑𝜓𝜒¬𝜃𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
9967	→→⋀⋀⋀𝜑𝜓𝜒𝜃¬→⋀⋀𝜑𝜓𝜒¬𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 9965, 9966
9968	→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 9768, 9967	simpllr
9969	→→𝜓→𝜃𝜓→⋀𝜓𝜒→𝜓→𝜃𝜓	Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
9970	→⋀𝜓𝜒→𝜓→𝜃𝜓	Modus ponens 9774, 9969
9971	→→⋀𝜓𝜒→𝜓→𝜃𝜓→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
9972	→→⋀𝜓𝜒𝜓→⋀𝜓𝜒→𝜃𝜓	Modus ponens 9970, 9971
9973	→⋀𝜓𝜒→𝜃𝜓	Modus ponens 6072, 9972
9974	↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into df-an
9975	→𝜃→⋀𝜓𝜒𝜃	Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒] into ax-1
9976	→→𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃	Subs [𝜑↗→𝜃→⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1
9977	→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃	Modus ponens 9975, 9976
9978	→→¬¬𝜃→𝜃→⋀𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜓𝜒𝜃	Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜓𝜒𝜃] into ax-2
9979	→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜓𝜒𝜃	Modus ponens 9977, 9978
9980	→¬¬𝜃→⋀𝜓𝜒𝜃	Modus ponens 9525, 9979
9981	→→⋀𝜓𝜒→𝜃𝜓→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
9982	→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓	Modus ponens 9973, 9981
9983	→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1
9984	→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓	Modus ponens 9982, 9983
9985	→→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
9986	→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜓	Modus ponens 9984, 9985
9987	→¬¬𝜃→⋀𝜓𝜒𝜓	Modus ponens 9980, 9986
9988	→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1
9989	→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
9990	→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒	Modus ponens 9988, 9989
9991	→→⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→¬¬𝜃⋀𝜓𝜒] into ax-2
9992	→→⋀𝜓𝜒⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒	Modus ponens 9990, 9991
9993	→→¬¬𝜃→⋀𝜓𝜒𝜓→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
9994	→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9987, 9993
9995	→→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
9996	→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9994, 9995
9997	→→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜓→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2
9998	→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9996, 9997
9999	→⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 9988, 9998
10000	→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
10001	→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Modus ponens 9797, 10000
10002	→→⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→¬¬𝜃¬¬𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
10003	→→⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜓𝜒→¬¬𝜃¬¬𝜓	Modus ponens 10001, 10002
10004	→⋀𝜓𝜒→¬¬𝜃¬¬𝜓	Modus ponens 9999, 10003
10005	→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-1
10006	→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Modus ponens 9803, 10005
10007	→→⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜃	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
10008	→→⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜓𝜒→¬𝜓¬𝜃	Modus ponens 10006, 10007
10009	→⋀𝜓𝜒→¬𝜓¬𝜃	Modus ponens 10004, 10008
10010	→→⋀𝜓𝜒→¬𝜓¬𝜃→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
10011	→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃	Modus ponens 10009, 10010
10012	→→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10013	→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃	Modus ponens 10011, 10012
10014	→→¬𝜓→→⋀𝜓𝜒¬𝜓→⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜓𝜒¬𝜃] into ax-2
10015	→→¬𝜓→⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜓𝜒¬𝜃	Modus ponens 10013, 10014
10016	→¬𝜓→⋀𝜓𝜒¬𝜃	Modus ponens 8964, 10015
10017	→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃] into id
10018	→→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10019	→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10017, 10018
10020	→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃] into notnotr
10021	→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10022	→→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10023	→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Modus ponens 10021, 10022
10024	→→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜃] into ax-2
10025	→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Modus ponens 10023, 10024
10026	→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Modus ponens 10020, 10025
10027	→→¬𝜓→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10028	→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Modus ponens 10019, 10027
10029	→→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10030	→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Modus ponens 10028, 10029
10031	→→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜓𝜒¬𝜃] into ax-2
10032	→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃	Modus ponens 10030, 10031
10033	→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10034	→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
10035	→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓	Modus ponens 10033, 10034
10036	→→¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓] into ax-2
10037	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓	Modus ponens 10035, 10036
10038	→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10039	→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10026, 10038
10040	→→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10041	→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10039, 10040
10042	→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃] into ax-2
10043	→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10041, 10042
10044	→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10033, 10043
10045	→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→⋀𝜓𝜒¬𝜃] into ax-3
10046	→→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10047	→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10045, 10046
10048	→→¬𝜓→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10049	→→¬𝜓→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10047, 10048
10050	→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10044, 10049
10051	→→¬𝜓→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10052	→→¬𝜓→⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10050, 10051
10053	→¬𝜓¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10016, 10052
10054	→→¬𝜓¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-3
10055	→¬→⋀𝜓𝜒¬𝜃𝜓	Modus ponens 10053, 10054
10056	→↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into biimp
10057	→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 9974, 10056
10058	→→¬→⋀𝜓𝜒¬𝜃𝜓→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10059	→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓	Modus ponens 10055, 10058
10060	→→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
10061	→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10059, 10060
10062	→⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10057, 10061
10063	→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒	Subs [𝜓↗⋀𝜓𝜒] into simpr
10064	→↔⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into bicom1
10065	↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃	Modus ponens 9974, 10064
10066	→↔¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into biimp
10067	→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃	Modus ponens 10065, 10066
10068	→→⋀⋀𝜓𝜒𝜃𝜓→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗→⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-1
10069	→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10062, 10068
10070	→→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜓→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
10071	→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜓	Modus ponens 10069, 10070
10072	→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into pm3.2im
10073	→→¬→⋀𝜓𝜒¬𝜃𝜓→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜓, 𝜓↗𝜃] into ax-1
10074	→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓	Modus ponens 10055, 10073
10075	→→𝜃→¬→⋀𝜓𝜒¬𝜃𝜓→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓	Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
10076	→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓	Modus ponens 10074, 10075
10077	→→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓	Subs [𝜑↗→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
10078	→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓	Modus ponens 10076, 10077
10079	→→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜓→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→𝜃𝜓] into ax-2
10080	→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜓	Modus ponens 10078, 10079
10081	→→𝜃→⋀𝜓𝜒𝜃→𝜃→𝜃→⋀𝜓𝜒𝜃	Subs [𝜑↗→𝜃→⋀𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1
10082	→𝜃→𝜃→⋀𝜓𝜒𝜃	Modus ponens 9975, 10081
10083	→→𝜃→𝜃→⋀𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀𝜓𝜒𝜃	Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜓𝜒𝜃] into ax-2
10084	→→𝜃𝜃→𝜃→⋀𝜓𝜒𝜃	Modus ponens 10082, 10083
10085	→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1
10086	→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓	Modus ponens 9982, 10085
10087	→→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜓→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜓	Subs [𝜑↗𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
10088	→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜓	Modus ponens 10086, 10087
10089	→𝜃→⋀𝜓𝜒𝜓	Modus ponens 9975, 10088
10090	→⋀𝜓𝜒→𝜃⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into ax-1
10091	→→⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→𝜃⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10092	→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒	Modus ponens 10090, 10091
10093	→→⋀𝜑⋀𝜓𝜒→⋀𝜓𝜒→𝜃⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜃⋀𝜓𝜒] into ax-2
10094	→→⋀𝜑⋀𝜓𝜒⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒	Modus ponens 10092, 10093
10095	→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒	Modus ponens 10063, 10094
10096	→→𝜃→⋀𝜓𝜒𝜓→→𝜃⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10097	→→𝜃⋀𝜓𝜒→𝜃𝜓	Modus ponens 10089, 10096
10098	→→→𝜃⋀𝜓𝜒→𝜃𝜓→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗→→𝜃⋀𝜓𝜒→𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10099	→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓	Modus ponens 10097, 10098
10100	→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
10101	→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓	Modus ponens 10099, 10100
10102	→⋀𝜑⋀𝜓𝜒→𝜃𝜓	Modus ponens 10095, 10101
10103	→𝜃→⋀𝜑⋀𝜓𝜒𝜃	Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10104	→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃	Subs [𝜑↗→𝜃→⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗𝜃] into ax-1
10105	→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃	Modus ponens 10103, 10104
10106	→→𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃→→𝜃𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃	Subs [𝜑↗𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜃] into ax-2
10107	→→𝜃𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃	Modus ponens 10105, 10106
10108	→→⋀𝜑⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃, 𝜒↗𝜓] into ax-2
10109	→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 10102, 10108
10110	→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗𝜃] into ax-1
10111	→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 10109, 10110
10112	→→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
10113	→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 10111, 10112
10114	→𝜃→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 10103, 10113
10115	→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into ax-1
10116	→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10117	→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒	Modus ponens 10115, 10116
10118	→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃⋀𝜑⋀𝜓𝜒] into ax-2
10119	→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒	Modus ponens 10117, 10118
10120	→→𝜃→⋀𝜑⋀𝜓𝜒𝜓→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10121	→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓	Modus ponens 10114, 10120
10122	→→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10123	→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓	Modus ponens 10121, 10122
10124	→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜓→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
10125	→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜓	Modus ponens 10123, 10124
10126	↔⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into df-an
10127	→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃	Subs [𝜑↗→𝜃→⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜃] into ax-1
10128	→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃	Modus ponens 10103, 10127
10129	→→¬¬𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜃→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃	Subs [𝜑↗¬¬𝜃, 𝜓↗𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜃] into ax-2
10130	→→¬¬𝜃𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃	Modus ponens 10128, 10129
10131	→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃	Modus ponens 9525, 10130
10132	→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗¬¬𝜃] into ax-1
10133	→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 10109, 10132
10134	→→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜓→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜓] into ax-2
10135	→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 10133, 10134
10136	→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens 10131, 10135
10137	→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬¬𝜃] into ax-1
10138	→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10139	→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒	Modus ponens 10137, 10138
10140	→→⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃⋀𝜑⋀𝜓𝜒] into ax-2
10141	→→⋀𝜑⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒	Modus ponens 10139, 10140
10142	→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜓→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10143	→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 10136, 10142
10144	→→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10145	→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 10143, 10144
10146	→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜓] into ax-2
10147	→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 10145, 10146
10148	→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓	Modus ponens 10137, 10147
10149	→→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Subs [𝜑↗→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10150	→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓	Modus ponens 9797, 10149
10151	→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜓→¬¬𝜃¬¬𝜓→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜓, 𝜒↗→¬¬𝜃¬¬𝜓] into ax-2
10152	→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜓→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓	Modus ponens 10150, 10151
10153	→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓	Modus ponens 10148, 10152
10154	→→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10155	→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃	Modus ponens 9803, 10154
10156	→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜓→¬𝜓¬𝜃→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜓, 𝜒↗→¬𝜓¬𝜃] into ax-2
10157	→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜓→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃	Modus ponens 10155, 10156
10158	→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃	Modus ponens 10153, 10157
10159	→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10160	→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓	Subs [𝜑↗→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓, 𝜓↗¬𝜓] into ax-1
10161	→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓	Modus ponens 10159, 10160
10162	→→¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜓] into ax-2
10163	→→¬𝜓¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓	Modus ponens 10161, 10162
10164	→→⋀𝜑⋀𝜓𝜒→¬𝜓¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜃] into ax-2
10165	→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10158, 10164
10166	→→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10167	→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10165, 10166
10168	→→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜓, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10169	→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜓→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10167, 10168
10170	→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10159, 10169
10171	→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into id
10172	→→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10173	→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10171, 10172
10174	→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into notnotr
10175	→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10176	→→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10177	→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10175, 10176
10178	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10179	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10177, 10178
10180	→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10174, 10179
10181	→→¬𝜓→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10182	→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10173, 10181
10183	→→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10184	→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10182, 10183
10185	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10186	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10184, 10185
10187	→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10188	→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
10189	→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓	Modus ponens 10187, 10188
10190	→→¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓] into ax-2
10191	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓	Modus ponens 10189, 10190
10192	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10193	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10180, 10192
10194	→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10195	→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10193, 10194
10196	→→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10197	→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜓→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10195, 10196
10198	→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10187, 10197
10199	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3
10200	→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜓] into ax-1
10201	→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10199, 10200
10202	→→¬𝜓→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10203	→→¬𝜓→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10201, 10202
10204	→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10198, 10203
10205	→→¬𝜓→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜓, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10206	→→¬𝜓→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10204, 10205
10207	→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10170, 10206
10208	→→¬𝜓¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3
10209	→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓	Modus ponens 10207, 10208
10210	→↔⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into biimp
10211	→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10126, 10210
10212	→→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓	Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓, 𝜓↗⋀⋀𝜑⋀𝜓𝜒𝜃] into ax-1
10213	→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓	Modus ponens 10209, 10212
10214	→→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜓→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗𝜓] into ax-2
10215	→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓	Modus ponens 10213, 10214
10216	→⋀⋀𝜑⋀𝜓𝜒𝜃𝜓	Modus ponens 10211, 10215	simplrl
10217	→𝜒→𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜃] into ax-1
10218	→→𝜒→𝜃𝜒→⋀𝜓𝜒→𝜒→𝜃𝜒	Subs [𝜑↗→𝜒→𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10219	→⋀𝜓𝜒→𝜒→𝜃𝜒	Modus ponens 10217, 10218
10220	→→⋀𝜓𝜒→𝜒→𝜃𝜒→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜒, 𝜒↗→𝜃𝜒] into ax-2
10221	→→⋀𝜓𝜒𝜒→⋀𝜓𝜒→𝜃𝜒	Modus ponens 10219, 10220
10222	→⋀𝜓𝜒→𝜃𝜒	Modus ponens 6077, 10221
10223	→→⋀𝜓𝜒→𝜃𝜒→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into ax-2
10224	→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒	Modus ponens 10222, 10223
10225	→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒	Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜃] into ax-1
10226	→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒	Modus ponens 10224, 10225
10227	→→¬¬𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜒	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
10228	→→¬¬𝜃→⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜓𝜒𝜒	Modus ponens 10226, 10227
10229	→¬¬𝜃→⋀𝜓𝜒𝜒	Modus ponens 9980, 10228
10230	→→¬¬𝜃→⋀𝜓𝜒𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-2
10231	→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 10229, 10230
10232	→→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒	Subs [𝜑↗→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10233	→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 10231, 10232
10234	→→⋀𝜓𝜒→→¬¬𝜃⋀𝜓𝜒→¬¬𝜃𝜒→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜒] into ax-2
10235	→→⋀𝜓𝜒→¬¬𝜃⋀𝜓𝜒→⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 10233, 10234
10236	→⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 9988, 10235
10237	→→𝜒¬¬𝜒→¬¬𝜃→𝜒¬¬𝜒	Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬𝜃] into ax-1
10238	→¬¬𝜃→𝜒¬¬𝜒	Modus ponens 9172, 10237
10239	→→¬¬𝜃→𝜒¬¬𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒	Subs [𝜑↗¬¬𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
10240	→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒	Modus ponens 10238, 10239
10241	→→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒	Subs [𝜑↗→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10242	→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒	Modus ponens 10240, 10241
10243	→→⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→→⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→¬¬𝜃¬¬𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜒, 𝜒↗→¬¬𝜃¬¬𝜒] into ax-2
10244	→→⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜓𝜒→¬¬𝜃¬¬𝜒	Modus ponens 10242, 10243
10245	→⋀𝜓𝜒→¬¬𝜃¬¬𝜒	Modus ponens 10236, 10244
10246	→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜒] into ax-3
10247	→→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃, 𝜓↗⋀𝜓𝜒] into ax-1
10248	→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃	Modus ponens 10246, 10247
10249	→→⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→→⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜃	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜒, 𝜒↗→¬𝜒¬𝜃] into ax-2
10250	→→⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜓𝜒→¬𝜒¬𝜃	Modus ponens 10248, 10249
10251	→⋀𝜓𝜒→¬𝜒¬𝜃	Modus ponens 10245, 10250
10252	→→⋀𝜓𝜒→¬𝜒¬𝜃→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜃] into ax-2
10253	→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃	Modus ponens 10251, 10252
10254	→→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10255	→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃	Modus ponens 10253, 10254
10256	→→¬𝜒→→⋀𝜓𝜒¬𝜒→⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜓𝜒¬𝜃] into ax-2
10257	→→¬𝜒→⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜓𝜒¬𝜃	Modus ponens 10255, 10256
10258	→¬𝜒→⋀𝜓𝜒¬𝜃	Modus ponens 9369, 10257
10259	→→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10260	→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10017, 10259
10261	→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10262	→→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10263	→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Modus ponens 10261, 10262
10264	→→¬¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜃] into ax-2
10265	→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Modus ponens 10263, 10264
10266	→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Modus ponens 10020, 10265
10267	→→¬𝜒→¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10268	→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Modus ponens 10260, 10267
10269	→→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10270	→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Modus ponens 10268, 10269
10271	→→¬¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜒¬→⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜓𝜒¬𝜃] into ax-2
10272	→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃	Modus ponens 10270, 10271
10273	→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓𝜒¬𝜃] into ax-1
10274	→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10275	→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒	Modus ponens 10273, 10274
10276	→→¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒] into ax-2
10277	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒	Modus ponens 10275, 10276
10278	→→¬¬¬→⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10279	→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10266, 10278
10280	→→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10281	→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10279, 10280
10282	→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒, 𝜒↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃] into ax-2
10283	→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10281, 10282
10284	→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃	Modus ponens 10273, 10283
10285	→→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10286	→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10045, 10285
10287	→→¬𝜒→→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10288	→→¬𝜒→¬¬¬→⋀𝜓𝜒¬𝜃¬→⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10286, 10287
10289	→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10284, 10288
10290	→→¬𝜒→→⋀𝜓𝜒¬𝜃¬¬→⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜓𝜒¬𝜃] into ax-2
10291	→→¬𝜒→⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10289, 10290
10292	→¬𝜒¬¬→⋀𝜓𝜒¬𝜃	Modus ponens 10258, 10291
10293	→→¬𝜒¬¬→⋀𝜓𝜒¬𝜃→¬→⋀𝜓𝜒¬𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-3
10294	→¬→⋀𝜓𝜒¬𝜃𝜒	Modus ponens 10292, 10293
10295	→→¬→⋀𝜓𝜒¬𝜃𝜒→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10296	→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒	Modus ponens 10294, 10295
10297	→→⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10298	→→⋀⋀𝜓𝜒𝜃¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10296, 10297
10299	→⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10057, 10298
10300	→→⋀⋀𝜓𝜒𝜃𝜒→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗→⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-1
10301	→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10299, 10300
10302	→→¬→⋀𝜓𝜒¬𝜃→⋀⋀𝜓𝜒𝜃𝜒→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒	Subs [𝜑↗¬→⋀𝜓𝜒¬𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-2
10303	→→¬→⋀𝜓𝜒¬𝜃⋀⋀𝜓𝜒𝜃→¬→⋀𝜓𝜒¬𝜃𝜒	Modus ponens 10301, 10302
10304	→→¬→⋀𝜓𝜒¬𝜃𝜒→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒	Subs [𝜑↗→¬→⋀𝜓𝜒¬𝜃𝜒, 𝜓↗𝜃] into ax-1
10305	→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒	Modus ponens 10294, 10304
10306	→→𝜃→¬→⋀𝜓𝜒¬𝜃𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒	Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓𝜒¬𝜃] into ax-2
10307	→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒	Modus ponens 10305, 10306
10308	→→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒	Subs [𝜑↗→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10309	→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒	Modus ponens 10307, 10308
10310	→→⋀𝜓𝜒→→𝜃¬→⋀𝜓𝜒¬𝜃→𝜃𝜒→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗→𝜃¬→⋀𝜓𝜒¬𝜃, 𝜒↗→𝜃𝜒] into ax-2
10311	→→⋀𝜓𝜒→𝜃¬→⋀𝜓𝜒¬𝜃→⋀𝜓𝜒→𝜃𝜒	Modus ponens 10309, 10310
10312	→→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒	Subs [𝜑↗→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒, 𝜓↗𝜃] into ax-1
10313	→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒	Modus ponens 10224, 10312
10314	→→𝜃→→⋀𝜓𝜒𝜃→⋀𝜓𝜒𝜒→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜒	Subs [𝜑↗𝜃, 𝜓↗→⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
10315	→→𝜃→⋀𝜓𝜒𝜃→𝜃→⋀𝜓𝜒𝜒	Modus ponens 10313, 10314
10316	→𝜃→⋀𝜓𝜒𝜒	Modus ponens 9975, 10315
10317	→→𝜃→⋀𝜓𝜒𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗𝜃, 𝜓↗⋀𝜓𝜒] into ax-2
10318	→→𝜃⋀𝜓𝜒→𝜃𝜒	Modus ponens 10316, 10317
10319	→→→𝜃⋀𝜓𝜒→𝜃𝜒→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗→→𝜃⋀𝜓𝜒→𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10320	→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒	Modus ponens 10318, 10319
10321	→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜓𝜒, 𝜒↗→𝜃𝜒] into ax-2
10322	→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒	Modus ponens 10320, 10321
10323	→⋀𝜑⋀𝜓𝜒→𝜃𝜒	Modus ponens 10095, 10322
10324	→→⋀𝜑⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗𝜃] into ax-2
10325	→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 10323, 10324
10326	→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒	Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗𝜃] into ax-1
10327	→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 10325, 10326
10328	→→𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜒	Subs [𝜑↗𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜒] into ax-2
10329	→→𝜃→⋀𝜑⋀𝜓𝜒𝜃→𝜃→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 10327, 10328
10330	→𝜃→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 10103, 10329
10331	→→𝜃→⋀𝜑⋀𝜓𝜒𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2
10332	→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒	Modus ponens 10330, 10331
10333	→→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10334	→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒	Modus ponens 10332, 10333
10335	→→⋀𝜑⋀𝜓𝜒→→𝜃⋀𝜑⋀𝜓𝜒→𝜃𝜒→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→𝜃𝜒] into ax-2
10336	→→⋀𝜑⋀𝜓𝜒→𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→𝜃𝜒	Modus ponens 10334, 10335
10337	→→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒	Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗¬¬𝜃] into ax-1
10338	→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 10325, 10337
10339	→→¬¬𝜃→→⋀𝜑⋀𝜓𝜒𝜃→⋀𝜑⋀𝜓𝜒𝜒→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒	Subs [𝜑↗¬¬𝜃, 𝜓↗→⋀𝜑⋀𝜓𝜒𝜃, 𝜒↗→⋀𝜑⋀𝜓𝜒𝜒] into ax-2
10340	→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜃→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 10338, 10339
10341	→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens 10131, 10340
10342	→→¬¬𝜃→⋀𝜑⋀𝜓𝜒𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒	Subs [𝜑↗¬¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2
10343	→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 10341, 10342
10344	→→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒	Subs [𝜑↗→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10345	→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 10343, 10344
10346	→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃⋀𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜃𝜒] into ax-2
10347	→→⋀𝜑⋀𝜓𝜒→¬¬𝜃⋀𝜑⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 10345, 10346
10348	→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒	Modus ponens 10137, 10347
10349	→→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒	Subs [𝜑↗→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10350	→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒	Modus ponens 10240, 10349
10351	→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃𝜒→¬¬𝜃¬¬𝜒→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃𝜒, 𝜒↗→¬¬𝜃¬¬𝜒] into ax-2
10352	→→⋀𝜑⋀𝜓𝜒→¬¬𝜃𝜒→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒	Modus ponens 10350, 10351
10353	→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒	Modus ponens 10348, 10352
10354	→→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃	Subs [𝜑↗→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10355	→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃	Modus ponens 10246, 10354
10356	→→⋀𝜑⋀𝜓𝜒→→¬¬𝜃¬¬𝜒→¬𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗→¬¬𝜃¬¬𝜒, 𝜒↗→¬𝜒¬𝜃] into ax-2
10357	→→⋀𝜑⋀𝜓𝜒→¬¬𝜃¬¬𝜒→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃	Modus ponens 10355, 10356
10358	→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃	Modus ponens 10353, 10357
10359	→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-1
10360	→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒	Subs [𝜑↗→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒, 𝜓↗¬𝜒] into ax-1
10361	→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒	Modus ponens 10359, 10360
10362	→→¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜒] into ax-2
10363	→→¬𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒	Modus ponens 10361, 10362
10364	→→⋀𝜑⋀𝜓𝜒→¬𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗⋀𝜑⋀𝜓𝜒, 𝜓↗¬𝜒, 𝜒↗¬𝜃] into ax-2
10365	→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10358, 10364
10366	→→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10367	→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10365, 10366
10368	→→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜒, 𝜒↗→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10369	→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜒→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10367, 10368
10370	→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10359, 10369
10371	→→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10372	→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10171, 10371
10373	→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10374	→→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10375	→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10373, 10374
10376	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10377	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10375, 10376
10378	→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10174, 10377
10379	→→¬𝜒→¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10380	→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10372, 10379
10381	→→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10382	→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10380, 10381
10383	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10384	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10382, 10383
10385	→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-1
10386	→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10387	→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒	Modus ponens 10385, 10386
10388	→→¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒] into ax-2
10389	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒	Modus ponens 10387, 10388
10390	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10391	→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10378, 10390
10392	→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10393	→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10391, 10392
10394	→→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒, 𝜒↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10395	→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬𝜒→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10393, 10394
10396	→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10385, 10395
10397	→→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜓↗¬𝜒] into ax-1
10398	→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10199, 10397
10399	→→¬𝜒→→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10400	→→¬𝜒→¬¬¬→⋀𝜑⋀𝜓𝜒¬𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10398, 10399
10401	→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10396, 10400
10402	→→¬𝜒→→⋀𝜑⋀𝜓𝜒¬𝜃¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜑⋀𝜓𝜒¬𝜃, 𝜒↗¬¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10403	→→¬𝜒→⋀𝜑⋀𝜓𝜒¬𝜃→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10401, 10402
10404	→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃	Modus ponens 10370, 10403
10405	→→¬𝜒¬¬→⋀𝜑⋀𝜓𝜒¬𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-3
10406	→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒	Modus ponens 10404, 10405
10407	→→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒	Subs [𝜑↗→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒, 𝜓↗⋀⋀𝜑⋀𝜓𝜒𝜃] into ax-1
10408	→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒	Modus ponens 10406, 10407
10409	→→⋀⋀𝜑⋀𝜓𝜒𝜃→¬→⋀𝜑⋀𝜓𝜒¬𝜃𝜒→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗⋀⋀𝜑⋀𝜓𝜒𝜃, 𝜓↗¬→⋀𝜑⋀𝜓𝜒¬𝜃] into ax-2
10410	→→⋀⋀𝜑⋀𝜓𝜒𝜃¬→⋀𝜑⋀𝜓𝜒¬𝜃→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒	Modus ponens 10408, 10409
10411	→⋀⋀𝜑⋀𝜓𝜒𝜃𝜒	Modus ponens 10211, 10410	simplrr
10412	→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜃] into simpl
10413	→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10414	→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 5001, 10413
10415	→→⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10416	→→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10414, 10415
10417	→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10412, 10416
10418	↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into df-an
10419	→𝜑→⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10420	→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜑↗→𝜑→⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜑] into ax-1
10421	→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10419, 10420
10422	→→¬¬𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10423	→→¬¬𝜑𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10421, 10422
10424	→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑	Modus ponens notnotr, 10423
10425	→→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10426	→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10417, 10425
10427	→→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1
10428	→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10426, 10427
10429	→→¬¬𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2
10430	→→¬¬𝜑→⋀⋀𝜓𝜒𝜃𝜑→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10428, 10429
10431	→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10424, 10430
10432	→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀⋀𝜓𝜒𝜃] into id
10433	→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬𝜑] into ax-1
10434	→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10435	→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃	Modus ponens 10433, 10434
10436	→→⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗→¬¬𝜑⋀⋀𝜓𝜒𝜃] into ax-2
10437	→→⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃	Modus ponens 10435, 10436
10438	→→¬¬𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2
10439	→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒	Modus ponens 10431, 10438
10440	→→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10441	→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒	Modus ponens 10439, 10440
10442	→→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗→¬¬𝜑⋀𝜓𝜒] into ax-2
10443	→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒	Modus ponens 10441, 10442
10444	→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒	Modus ponens 10433, 10443
10445	→⋀𝜓𝜒¬¬⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒] into notnot
10446	→→⋀𝜓𝜒¬¬⋀𝜓𝜒→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒¬¬⋀𝜓𝜒, 𝜓↗¬¬𝜑] into ax-1
10447	→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒	Modus ponens 10445, 10446
10448	→→¬¬𝜑→⋀𝜓𝜒¬¬⋀𝜓𝜒→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓𝜒, 𝜒↗¬¬⋀𝜓𝜒] into ax-2
10449	→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒	Modus ponens 10447, 10448
10450	→→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10451	→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒	Modus ponens 10449, 10450
10452	→→⋀⋀𝜓𝜒𝜃→→¬¬𝜑⋀𝜓𝜒→¬¬𝜑¬¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓𝜒, 𝜒↗→¬¬𝜑¬¬⋀𝜓𝜒] into ax-2
10453	→→⋀⋀𝜓𝜒𝜃→¬¬𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒	Modus ponens 10451, 10452
10454	→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒	Modus ponens 10444, 10453
10455	→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-3
10456	→→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10457	→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑	Modus ponens 10455, 10456
10458	→→⋀⋀𝜓𝜒𝜃→→¬¬𝜑¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬𝜑→→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→¬¬𝜑¬¬⋀𝜓𝜒, 𝜒↗→¬⋀𝜓𝜒¬𝜑] into ax-2
10459	→→⋀⋀𝜓𝜒𝜃→¬¬𝜑¬¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑	Modus ponens 10457, 10458
10460	→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑	Modus ponens 10454, 10459
10461	→¬⋀𝜓𝜒¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒] into id
10462	→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10463	→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Subs [𝜑↗→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10464	→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Modus ponens 10462, 10463
10465	→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒] into ax-2
10466	→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Modus ponens 10464, 10465
10467	→→⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬𝜑→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬𝜑] into ax-2
10468	→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10460, 10467
10469	→→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10470	→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10468, 10469
10471	→→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜒↗→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10472	→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10470, 10471
10473	→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10462, 10472
10474	→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into id
10475	→→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10476	→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10474, 10475
10477	→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into notnotr
10478	→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10479	→→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10480	→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10478, 10479
10481	→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10482	→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10480, 10481
10483	→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10477, 10482
10484	→→¬⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10485	→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10476, 10484
10486	→→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10487	→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10485, 10486
10488	→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10489	→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10487, 10488
10490	→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10491	→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10492	→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒	Modus ponens 10490, 10491
10493	→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒] into ax-2
10494	→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒	Modus ponens 10492, 10493
10495	→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10496	→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10483, 10495
10497	→→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10498	→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10496, 10497
10499	→→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒, 𝜒↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10500	→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10498, 10499
10501	→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10490, 10500
10502	→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-3
10503	→→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗¬⋀𝜓𝜒] into ax-1
10504	→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10502, 10503
10505	→→¬⋀𝜓𝜒→→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10506	→→¬⋀𝜓𝜒→¬¬¬→⋀⋀𝜓𝜒𝜃¬𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10504, 10505
10507	→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10501, 10506
10508	→→¬⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃¬𝜑¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-2
10509	→→¬⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃¬𝜑→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10507, 10508
10510	→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10473, 10509
10511	→→¬⋀𝜓𝜒¬¬→⋀⋀𝜓𝜒𝜃¬𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-3
10512	→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Modus ponens 10510, 10511
10513	→↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into biimp
10514	→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Modus ponens 10418, 10513
10515	→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑] into ax-1
10516	→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Modus ponens 10512, 10515
10517	→→⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10518	→→⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒	Modus ponens 10516, 10517
10519	→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒	Modus ponens 10514, 10518
10520	→↔⋀⋀⋀𝜓𝜒𝜃𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜑↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into bicom1
10521	↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10418, 10520
10522	→↔¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑] into biimp
10523	→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10521, 10522
10524	→→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒, 𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑] into ax-1
10525	→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒	Modus ponens 10519, 10524
10526	→→¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜓𝜒𝜃𝜑⋀𝜓𝜒→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Subs [𝜑↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜓↗⋀⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10527	→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀⋀⋀𝜓𝜒𝜃𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Modus ponens 10525, 10526
10528	→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into pm3.2im
10529	→→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Subs [𝜑↗→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10530	→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒	Modus ponens 10512, 10529
10531	→→𝜑→¬→⋀⋀𝜓𝜒𝜃¬𝜑⋀𝜓𝜒→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒	Subs [𝜓↗¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10532	→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒	Modus ponens 10530, 10531
10533	→→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒, 𝜓↗⋀⋀𝜓𝜒𝜃] into ax-1
10534	→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒	Modus ponens 10532, 10533
10535	→→⋀⋀𝜓𝜒𝜃→→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→𝜑⋀𝜓𝜒→→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10536	→→⋀⋀𝜓𝜒𝜃→𝜑¬→⋀⋀𝜓𝜒𝜃¬𝜑→⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10534, 10535
10537	→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜑↗→𝜑→⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
10538	→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10419, 10537
10539	→→𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜓↗𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10540	→→𝜑𝜑→𝜑→⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10538, 10539
10541	→→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10542	→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10426, 10541
10543	→→𝜑→→⋀⋀𝜓𝜒𝜃𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜓↗→⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2
10544	→→𝜑→⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10542, 10543
10545	→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10419, 10544
10546	↔⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into df-an
10547	→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀⋀𝜓𝜒𝜃] into notnotr
10548	→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-1
10549	→→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10550	→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃	Modus ponens 10548, 10549
10551	→→¬¬⋀⋀𝜓𝜒𝜃→⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗→𝜑⋀⋀𝜓𝜒𝜃] into ax-2
10552	→→¬¬⋀⋀𝜓𝜒𝜃⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃	Modus ponens 10550, 10551
10553	→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃	Modus ponens 10547, 10552
10554	→→𝜑→⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Subs [𝜓↗⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2
10555	→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10545, 10554
10556	→→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10557	→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10555, 10556
10558	→→¬¬⋀⋀𝜓𝜒𝜃→→𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10559	→→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀⋀𝜓𝜒𝜃→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10557, 10558
10560	→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10553, 10559
10561	→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10562	→→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜑↗→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
10563	→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10561, 10562
10564	→→𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10565	→→𝜑𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10563, 10564
10566	→→¬¬⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into ax-2
10567	→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10560, 10566
10568	→→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10569	→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10567, 10568
10570	→→𝜑→→¬¬⋀⋀𝜓𝜒𝜃𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒] into ax-2
10571	→→𝜑→¬¬⋀⋀𝜓𝜒𝜃𝜑→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10569, 10570
10572	→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10561, 10571
10573	→→⋀𝜓𝜒¬¬⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒¬¬⋀𝜓𝜒, 𝜓↗¬¬⋀⋀𝜓𝜒𝜃] into ax-1
10574	→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒	Modus ponens 10445, 10573
10575	→→¬¬⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒¬¬⋀𝜓𝜒→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒	Subs [𝜑↗¬¬⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗¬¬⋀𝜓𝜒] into ax-2
10576	→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒	Modus ponens 10574, 10575
10577	→→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒	Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10578	→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒	Modus ponens 10576, 10577
10579	→→𝜑→→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒	Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜒↗→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒] into ax-2
10580	→→𝜑→¬¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒	Modus ponens 10578, 10579
10581	→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒	Modus ponens 10572, 10580
10582	→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-3
10583	→→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-1
10584	→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃	Modus ponens 10582, 10583
10585	→→𝜑→→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃	Subs [𝜓↗→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒, 𝜒↗→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃] into ax-2
10586	→→𝜑→¬¬⋀⋀𝜓𝜒𝜃¬¬⋀𝜓𝜒→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃	Modus ponens 10584, 10585
10587	→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃	Modus ponens 10581, 10586
10588	→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
10589	→→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10590	→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 10588, 10589
10591	→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
10592	→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 10590, 10591
10593	→→𝜑→¬⋀𝜓𝜒¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜓↗¬⋀𝜓𝜒, 𝜒↗¬⋀⋀𝜓𝜒𝜃] into ax-2
10594	→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10587, 10593
10595	→→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10596	→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10594, 10595
10597	→→¬⋀𝜓𝜒→→𝜑¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10598	→→¬⋀𝜓𝜒→𝜑¬⋀𝜓𝜒→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10596, 10597
10599	→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10588, 10598
10600	→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into id
10601	→→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10602	→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10600, 10601
10603	→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into notnotr
10604	→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10605	→→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1
10606	→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10604, 10605
10607	→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10608	→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10606, 10607
10609	→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10603, 10608
10610	→→¬⋀𝜓𝜒→¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10611	→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10602, 10610
10612	→→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1
10613	→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10611, 10612
10614	→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10615	→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10613, 10614
10616	→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-1
10617	→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Subs [𝜑↗→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒] into ax-1
10618	→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Modus ponens 10616, 10617
10619	→→¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗¬⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒] into ax-2
10620	→→¬⋀𝜓𝜒¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒	Modus ponens 10618, 10619
10621	→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒, 𝜒↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10622	→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10609, 10621
10623	→→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10624	→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10622, 10623
10625	→→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒, 𝜒↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10626	→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬⋀𝜓𝜒→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10624, 10625
10627	→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10616, 10626
10628	→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-3
10629	→→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜓↗¬⋀𝜓𝜒] into ax-1
10630	→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10628, 10629
10631	→→¬⋀𝜓𝜒→→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10632	→→¬⋀𝜓𝜒→¬¬¬→𝜑¬⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10630, 10631
10633	→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10627, 10632
10634	→→¬⋀𝜓𝜒→→𝜑¬⋀⋀𝜓𝜒𝜃¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗¬⋀𝜓𝜒, 𝜓↗→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-2
10635	→→¬⋀𝜓𝜒→𝜑¬⋀⋀𝜓𝜒𝜃→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10633, 10634
10636	→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10599, 10635
10637	→→¬⋀𝜓𝜒¬¬→𝜑¬⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into ax-3
10638	→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10636, 10637
10639	→↔⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃] into biimp
10640	→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃	Modus ponens 10546, 10639
10641	→→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10642	→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10638, 10641
10643	→→⋀𝜑⋀⋀𝜓𝜒𝜃→¬→𝜑¬⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗¬→𝜑¬⋀⋀𝜓𝜒𝜃, 𝜒↗⋀𝜓𝜒] into ax-2
10644	→→⋀𝜑⋀⋀𝜓𝜒𝜃¬→𝜑¬⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10642, 10643
10645	→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒	Modus ponens 10640, 10644
10646	→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜓↗⋀⋀𝜓𝜒𝜃] into simpl
10647	→→⋀𝜑⋀𝜓𝜒𝜓→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒𝜓, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1
10648	→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓	Modus ponens simprl, 10647
10649	→→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜓→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10650	→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓	Modus ponens 10648, 10649
10651	→→¬→𝜑¬⋀𝜓𝜒𝜓→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜓, 𝜓↗⋀𝜓𝜒] into ax-1
10652	→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓	Modus ponens 9112, 10651
10653	→→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜓→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒, 𝜒↗𝜓] into ax-2
10654	→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓	Modus ponens 10652, 10653
10655	→→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓	Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓, 𝜓↗𝜑] into ax-1
10656	→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓	Modus ponens 10654, 10655
10657	→→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜓→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜓	Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒𝜓] into ax-2
10658	→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜓	Modus ponens 10656, 10657
10659	→→⋀𝜓𝜒→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10660	→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒	Modus ponens 5001, 10659
10661	→→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜓𝜒→𝜑⋀𝜓𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜓𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
10662	→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10660, 10661
10663	→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒	Modus ponens 10645, 10662
10664	→→→𝜑⋀𝜓𝜒→𝜑𝜓→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜓, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10665	→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 6076, 10664
10666	→→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
10667	→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓	Modus ponens 10665, 10666
10668	→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓	Modus ponens 10663, 10667
10669	→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10670	→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
10671	→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10669, 10670
10672	→→𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑	Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑] into ax-2
10673	→→𝜑𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑	Modus ponens 10671, 10672
10674	→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
10675	→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10668, 10674
10676	→→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗𝜑] into ax-1
10677	→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10675, 10676
10678	→→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜓↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓] into ax-2
10679	→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10677, 10678
10680	→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10669, 10679
10681	→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10682	→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10680, 10681
10683	→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓] into ax-2
10684	→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10682, 10683
10685	→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10646, 10684
10686	→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃] into id
10687	→→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
10688	→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10685, 10687
10689	→⋀𝜑⋀⋀𝜓𝜒𝜃𝜓	Modus ponens 10686, 10688	simprll
10690	→→⋀𝜑⋀𝜓𝜒𝜒→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒	Subs [𝜑↗→⋀𝜑⋀𝜓𝜒𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-1
10691	→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒	Modus ponens simprr, 10690
10692	→→¬→𝜑¬⋀𝜓𝜒→⋀𝜑⋀𝜓𝜒𝜒→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒	Subs [𝜑↗¬→𝜑¬⋀𝜓𝜒, 𝜓↗⋀𝜑⋀𝜓𝜒] into ax-2
10693	→→¬→𝜑¬⋀𝜓𝜒⋀𝜑⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒	Modus ponens 10691, 10692
10694	→→¬→𝜑¬⋀𝜓𝜒𝜒→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓𝜒𝜒, 𝜓↗⋀𝜓𝜒] into ax-1
10695	→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒	Modus ponens 9512, 10694
10696	→→⋀𝜓𝜒→¬→𝜑¬⋀𝜓𝜒𝜒→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗¬→𝜑¬⋀𝜓𝜒] into ax-2
10697	→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒	Modus ponens 10695, 10696
10698	→→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒	Subs [𝜑↗→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒, 𝜓↗𝜑] into ax-1
10699	→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒	Modus ponens 10697, 10698
10700	→→𝜑→→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒𝜒→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜒	Subs [𝜓↗→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒𝜒] into ax-2
10701	→→𝜑→⋀𝜓𝜒¬→𝜑¬⋀𝜓𝜒→𝜑→⋀𝜓𝜒𝜒	Modus ponens 10699, 10700
10702	→→→𝜑⋀𝜓𝜒→𝜑𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒	Subs [𝜑↗→→𝜑⋀𝜓𝜒→𝜑𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10703	→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒	Modus ponens 6081, 10702
10704	→→⋀𝜑⋀⋀𝜓𝜒𝜃→→𝜑⋀𝜓𝜒→𝜑𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗→𝜑⋀𝜓𝜒, 𝜒↗→𝜑𝜒] into ax-2
10705	→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑⋀𝜓𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒	Modus ponens 10703, 10704
10706	→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒	Modus ponens 10663, 10705
10707	→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑] into ax-2
10708	→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10706, 10707
10709	→→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1
10710	→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10708, 10709
10711	→→𝜑→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜓↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒] into ax-2
10712	→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10710, 10711
10713	→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10669, 10712
10714	→→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-1
10715	→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10713, 10714
10716	→→⋀𝜑⋀⋀𝜓𝜒𝜃→𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒] into ax-2
10717	→→⋀𝜑⋀⋀𝜓𝜒𝜃𝜑→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10715, 10716
10718	→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10646, 10717
10719	→→⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Subs [𝜑↗⋀𝜑⋀⋀𝜓𝜒𝜃, 𝜓↗⋀𝜑⋀⋀𝜓𝜒𝜃] into ax-2
10720	→→⋀𝜑⋀⋀𝜓𝜒𝜃⋀𝜑⋀⋀𝜓𝜒𝜃→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10718, 10719
10721	→⋀𝜑⋀⋀𝜓𝜒𝜃𝜒	Modus ponens 10686, 10720	simprlr
10722	→⋀𝜒𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜃] into simpl
10723	→→𝜒→𝜓𝜒→⋀𝜒𝜃→𝜒→𝜓𝜒	Subs [𝜑↗→𝜒→𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10724	→⋀𝜒𝜃→𝜒→𝜓𝜒	Modus ponens 5362, 10723
10725	→→⋀𝜒𝜃→𝜒→𝜓𝜒→→⋀𝜒𝜃𝜒→⋀𝜒𝜃→𝜓𝜒	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗→𝜓𝜒] into ax-2
10726	→→⋀𝜒𝜃𝜒→⋀𝜒𝜃→𝜓𝜒	Modus ponens 10724, 10725
10727	→⋀𝜒𝜃→𝜓𝜒	Modus ponens 10722, 10726
10728	↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗⋀𝜒𝜃] into df-an
10729	→𝜓→⋀𝜒𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into ax-1
10730	→→𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓	Subs [𝜑↗→𝜓→⋀𝜒𝜃𝜓, 𝜓↗¬¬𝜓] into ax-1
10731	→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓	Modus ponens 10729, 10730
10732	→→¬¬𝜓→𝜓→⋀𝜒𝜃𝜓→→¬¬𝜓𝜓→¬¬𝜓→⋀𝜒𝜃𝜓	Subs [𝜑↗¬¬𝜓, 𝜒↗→⋀𝜒𝜃𝜓] into ax-2
10733	→→¬¬𝜓𝜓→¬¬𝜓→⋀𝜒𝜃𝜓	Modus ponens 10731, 10732
10734	→¬¬𝜓→⋀𝜒𝜃𝜓	Modus ponens 570, 10733
10735	→→⋀𝜒𝜃→𝜓𝜒→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒	Subs [𝜑↗⋀𝜒𝜃] into ax-2
10736	→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒	Modus ponens 10727, 10735
10737	→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒	Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒, 𝜓↗¬¬𝜓] into ax-1
10738	→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒	Modus ponens 10736, 10737
10739	→→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜒] into ax-2
10740	→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜒	Modus ponens 10738, 10739
10741	→¬¬𝜓→⋀𝜒𝜃𝜒	Modus ponens 10734, 10740
10742	→⋀𝜒𝜃⋀𝜒𝜃	Subs [𝜑↗⋀𝜒𝜃] into id
10743	→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬¬𝜓] into ax-1
10744	→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
10745	→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃	Modus ponens 10743, 10744
10746	→→⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→→⋀𝜒𝜃⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃, 𝜒↗→¬¬𝜓⋀𝜒𝜃] into ax-2
10747	→→⋀𝜒𝜃⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃	Modus ponens 10745, 10746
10748	→→¬¬𝜓→⋀𝜒𝜃𝜒→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒	Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-2
10749	→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒	Modus ponens 10741, 10748
10750	→→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒	Subs [𝜑↗→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10751	→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒	Modus ponens 10749, 10750
10752	→→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜒→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜒	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜓𝜒] into ax-2
10753	→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜒	Modus ponens 10751, 10752
10754	→⋀𝜒𝜃→¬¬𝜓𝜒	Modus ponens 10743, 10753
10755	→→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒	Subs [𝜑↗→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10756	→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒	Modus ponens 9176, 10755
10757	→→⋀𝜒𝜃→→¬¬𝜓𝜒→¬¬𝜓¬¬𝜒→→⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→¬¬𝜓¬¬𝜒	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓𝜒, 𝜒↗→¬¬𝜓¬¬𝜒] into ax-2
10758	→→⋀𝜒𝜃→¬¬𝜓𝜒→⋀𝜒𝜃→¬¬𝜓¬¬𝜒	Modus ponens 10756, 10757
10759	→⋀𝜒𝜃→¬¬𝜓¬¬𝜒	Modus ponens 10754, 10758
10760	→→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-1
10761	→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓	Modus ponens 9182, 10760
10762	→→⋀𝜒𝜃→→¬¬𝜓¬¬𝜒→¬𝜒¬𝜓→→⋀𝜒𝜃→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→¬𝜒¬𝜓	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓¬¬𝜒, 𝜒↗→¬𝜒¬𝜓] into ax-2
10763	→→⋀𝜒𝜃→¬¬𝜓¬¬𝜒→⋀𝜒𝜃→¬𝜒¬𝜓	Modus ponens 10761, 10762
10764	→⋀𝜒𝜃→¬𝜒¬𝜓	Modus ponens 10759, 10763
10765	→¬𝜒→⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10766	→→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒	Subs [𝜑↗→¬𝜒→⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10767	→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒	Modus ponens 10765, 10766
10768	→→¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜒𝜃¬𝜒] into ax-2
10769	→→¬𝜒¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜒	Modus ponens 10767, 10768
10770	→→⋀𝜒𝜃→¬𝜒¬𝜓→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬𝜓] into ax-2
10771	→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓	Modus ponens 10764, 10770
10772	→→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10773	→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓	Modus ponens 10771, 10772
10774	→→¬𝜒→→⋀𝜒𝜃¬𝜒→⋀𝜒𝜃¬𝜓→→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜒𝜃¬𝜒, 𝜒↗→⋀𝜒𝜃¬𝜓] into ax-2
10775	→→¬𝜒→⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜒𝜃¬𝜓	Modus ponens 10773, 10774
10776	→¬𝜒→⋀𝜒𝜃¬𝜓	Modus ponens 10765, 10775
10777	→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓] into id
10778	→→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10779	→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 10777, 10778
10780	→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓] into notnotr
10781	→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10782	→→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
10783	→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Modus ponens 10781, 10782
10784	→→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜒¬→⋀𝜒𝜃¬𝜓] into ax-2
10785	→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Modus ponens 10783, 10784
10786	→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Modus ponens 10780, 10785
10787	→→¬𝜒→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10788	→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Modus ponens 10779, 10787
10789	→→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
10790	→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Modus ponens 10788, 10789
10791	→→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→¬𝜒¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜒¬→⋀𝜒𝜃¬𝜓] into ax-2
10792	→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓	Modus ponens 10790, 10791
10793	→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
10794	→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒, 𝜓↗¬𝜒] into ax-1
10795	→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒	Modus ponens 10793, 10794
10796	→→¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒] into ax-2
10797	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒	Modus ponens 10795, 10796
10798	→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜒¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10799	→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 10786, 10798
10800	→→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10801	→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 10799, 10800
10802	→→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓] into ax-2
10803	→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜒→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 10801, 10802
10804	→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 10793, 10803
10805	→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→⋀𝜒𝜃¬𝜓] into ax-3
10806	→→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜒] into ax-1
10807	→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 10805, 10806
10808	→→¬𝜒→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓] into ax-2
10809	→→¬𝜒→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 10807, 10808
10810	→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 10804, 10809
10811	→→¬𝜒→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒¬¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜒𝜃¬𝜓, 𝜒↗¬¬→⋀𝜒𝜃¬𝜓] into ax-2
10812	→→¬𝜒→⋀𝜒𝜃¬𝜓→¬𝜒¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 10810, 10811
10813	→¬𝜒¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 10776, 10812
10814	→→¬𝜒¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-3
10815	→¬→⋀𝜒𝜃¬𝜓𝜒	Modus ponens 10813, 10814
10816	→↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into biimp
10817	→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 10728, 10816
10818	→→¬→⋀𝜒𝜃¬𝜓𝜒→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜒, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-1
10819	→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒	Modus ponens 10815, 10818
10820	→→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒	Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10821	→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒	Modus ponens 10819, 10820
10822	→⋀⋀𝜒𝜃𝜓𝜒	Modus ponens 10817, 10821
10823	→↔⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓	Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into bicom1
10824	↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓	Modus ponens 10728, 10823
10825	→↔¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓	Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓] into biimp
10826	→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓	Modus ponens 10824, 10825
10827	→→⋀⋀𝜒𝜃𝜓𝜒→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒	Subs [𝜑↗→⋀⋀𝜒𝜃𝜓𝜒, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-1
10828	→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒	Modus ponens 10822, 10827
10829	→→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜒→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒	Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-2
10830	→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜒	Modus ponens 10828, 10829
10831	→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗⋀𝜒𝜃] into pm3.2im
10832	→→¬→⋀𝜒𝜃¬𝜓𝜒→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜒] into ax-1
10833	→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒	Modus ponens 10815, 10832
10834	→→𝜓→¬→⋀𝜒𝜃¬𝜓𝜒→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-2
10835	→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒	Modus ponens 10833, 10834
10836	→→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒	Subs [𝜑↗→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒, 𝜓↗⋀𝜒𝜃] into ax-1
10837	→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒	Modus ponens 10835, 10836
10838	→→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜒→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜒	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→𝜓𝜒] into ax-2
10839	→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜒	Modus ponens 10837, 10838
10840	→→𝜓→⋀𝜒𝜃𝜓→𝜓→𝜓→⋀𝜒𝜃𝜓	Subs [𝜑↗→𝜓→⋀𝜒𝜃𝜓] into ax-1
10841	→𝜓→𝜓→⋀𝜒𝜃𝜓	Modus ponens 10729, 10840
10842	→→𝜓→𝜓→⋀𝜒𝜃𝜓→→𝜓𝜓→𝜓→⋀𝜒𝜃𝜓	Subs [𝜑↗𝜓, 𝜒↗→⋀𝜒𝜃𝜓] into ax-2
10843	→→𝜓𝜓→𝜓→⋀𝜒𝜃𝜓	Modus ponens 10841, 10842
10844	→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒	Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒] into ax-1
10845	→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒	Modus ponens 10736, 10844
10846	→→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜒→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜒	Subs [𝜑↗𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜒] into ax-2
10847	→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜒	Modus ponens 10845, 10846
10848	→𝜓→⋀𝜒𝜃𝜒	Modus ponens 10729, 10847
10849	↔⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into df-an
10850	→¬¬⋀𝜒𝜃⋀𝜒𝜃	Subs [𝜑↗⋀𝜒𝜃] into notnotr
10851	→⋀𝜒𝜃→𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜒𝜃] into ax-1
10852	→→⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀𝜒𝜃→𝜓⋀𝜒𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10853	→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃	Modus ponens 10851, 10852
10854	→→¬¬⋀𝜒𝜃→⋀𝜒𝜃→𝜓⋀𝜒𝜃→→¬¬⋀𝜒𝜃⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗⋀𝜒𝜃, 𝜒↗→𝜓⋀𝜒𝜃] into ax-2
10855	→→¬¬⋀𝜒𝜃⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃	Modus ponens 10853, 10854
10856	→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃	Modus ponens 10850, 10855
10857	→→𝜓→⋀𝜒𝜃𝜒→→𝜓⋀𝜒𝜃→𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃] into ax-2
10858	→→𝜓⋀𝜒𝜃→𝜓𝜒	Modus ponens 10848, 10857
10859	→→→𝜓⋀𝜒𝜃→𝜓𝜒→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒	Subs [𝜑↗→→𝜓⋀𝜒𝜃→𝜓𝜒, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10860	→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒	Modus ponens 10858, 10859
10861	→→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜒→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜒	Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗→𝜓⋀𝜒𝜃, 𝜒↗→𝜓𝜒] into ax-2
10862	→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜒	Modus ponens 10860, 10861
10863	→¬¬⋀𝜒𝜃→𝜓𝜒	Modus ponens 10856, 10862
10864	→𝜓→¬¬⋀𝜒𝜃𝜓	Subs [𝜑↗𝜓, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10865	→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓	Subs [𝜑↗→𝜓→¬¬⋀𝜒𝜃𝜓] into ax-1
10866	→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓	Modus ponens 10864, 10865
10867	→→𝜓→𝜓→¬¬⋀𝜒𝜃𝜓→→𝜓𝜓→𝜓→¬¬⋀𝜒𝜃𝜓	Subs [𝜑↗𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜓] into ax-2
10868	→→𝜓𝜓→𝜓→¬¬⋀𝜒𝜃𝜓	Modus ponens 10866, 10867
10869	→→¬¬⋀𝜒𝜃→𝜓𝜒→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒	Subs [𝜑↗¬¬⋀𝜒𝜃] into ax-2
10870	→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒	Modus ponens 10863, 10869
10871	→→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒	Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒] into ax-1
10872	→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒	Modus ponens 10870, 10871
10873	→→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜒→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜒] into ax-2
10874	→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜒	Modus ponens 10872, 10873
10875	→𝜓→¬¬⋀𝜒𝜃𝜒	Modus ponens 10864, 10874
10876	→→𝜒¬¬𝜒→¬¬⋀𝜒𝜃→𝜒¬¬𝜒	Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
10877	→¬¬⋀𝜒𝜃→𝜒¬¬𝜒	Modus ponens 9172, 10876
10878	→→¬¬⋀𝜒𝜃→𝜒¬¬𝜒→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒	Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
10879	→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒	Modus ponens 10877, 10878
10880	→→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒	Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒] into ax-1
10881	→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒	Modus ponens 10879, 10880
10882	→→𝜓→→¬¬⋀𝜒𝜃𝜒→¬¬⋀𝜒𝜃¬¬𝜒→→𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→¬¬⋀𝜒𝜃¬¬𝜒	Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜒, 𝜒↗→¬¬⋀𝜒𝜃¬¬𝜒] into ax-2
10883	→→𝜓→¬¬⋀𝜒𝜃𝜒→𝜓→¬¬⋀𝜒𝜃¬¬𝜒	Modus ponens 10881, 10882
10884	→𝜓→¬¬⋀𝜒𝜃¬¬𝜒	Modus ponens 10875, 10883
10885	→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃	Subs [𝜑↗¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-3
10886	→→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃	Subs [𝜑↗→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃] into ax-1
10887	→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃	Modus ponens 10885, 10886
10888	→→𝜓→→¬¬⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜒𝜃→→𝜓→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→¬𝜒¬⋀𝜒𝜃	Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜒𝜃] into ax-2
10889	→→𝜓→¬¬⋀𝜒𝜃¬¬𝜒→𝜓→¬𝜒¬⋀𝜒𝜃	Modus ponens 10887, 10888
10890	→𝜓→¬𝜒¬⋀𝜒𝜃	Modus ponens 10884, 10889
10891	→→𝜓→¬𝜒¬⋀𝜒𝜃→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃	Subs [𝜑↗𝜓, 𝜓↗¬𝜒, 𝜒↗¬⋀𝜒𝜃] into ax-2
10892	→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃	Modus ponens 10890, 10891
10893	→→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10894	→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃	Modus ponens 10892, 10893
10895	→→¬𝜒→→𝜓¬𝜒→𝜓¬⋀𝜒𝜃→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬𝜒, 𝜒↗→𝜓¬⋀𝜒𝜃] into ax-2
10896	→→¬𝜒→𝜓¬𝜒→¬𝜒→𝜓¬⋀𝜒𝜃	Modus ponens 10894, 10895
10897	→¬𝜒→𝜓¬⋀𝜒𝜃	Modus ponens 9284, 10896
10898	→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃] into id
10899	→→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10900	→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10898, 10899
10901	→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃] into notnotr
10902	→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10903	→→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
10904	→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Modus ponens 10902, 10903
10905	→→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜓¬⋀𝜒𝜃] into ax-2
10906	→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Modus ponens 10904, 10905
10907	→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Modus ponens 10901, 10906
10908	→→¬𝜒→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
10909	→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Modus ponens 10900, 10908
10910	→→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
10911	→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Modus ponens 10909, 10910
10912	→→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→¬𝜒¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜓¬⋀𝜒𝜃] into ax-2
10913	→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃	Modus ponens 10911, 10912
10914	→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
10915	→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10916	→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒	Modus ponens 10914, 10915
10917	→→¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒] into ax-2
10918	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒	Modus ponens 10916, 10917
10919	→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜒¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
10920	→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10907, 10919
10921	→→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10922	→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10920, 10921
10923	→→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
10924	→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10922, 10923
10925	→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10914, 10924
10926	→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→𝜓¬⋀𝜒𝜃] into ax-3
10927	→→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
10928	→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 10926, 10927
10929	→→¬𝜒→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃] into ax-2
10930	→→¬𝜒→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 10928, 10929
10931	→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 10925, 10930
10932	→→¬𝜒→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒¬¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→𝜓¬⋀𝜒𝜃, 𝜒↗¬¬→𝜓¬⋀𝜒𝜃] into ax-2
10933	→→¬𝜒→𝜓¬⋀𝜒𝜃→¬𝜒¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 10931, 10932
10934	→¬𝜒¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 10897, 10933
10935	→→¬𝜒¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-3
10936	→¬→𝜓¬⋀𝜒𝜃𝜒	Modus ponens 10934, 10935
10937	→↔⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into biimp
10938	→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10849, 10937
10939	→→¬→𝜓¬⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒	Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10940	→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒	Modus ponens 10936, 10939
10941	→→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜒→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-2
10942	→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10940, 10941
10943	→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10938, 10942
10944	→→𝜒→𝜑𝜒→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒	Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10945	→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒	Modus ponens 1834, 10944
10946	→→⋀𝜓⋀𝜒𝜃→𝜒→𝜑𝜒→→⋀𝜓⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
10947	→→⋀𝜓⋀𝜒𝜃𝜒→⋀𝜓⋀𝜒𝜃→𝜑𝜒	Modus ponens 10945, 10946
10948	→⋀𝜓⋀𝜒𝜃→𝜑𝜒	Modus ponens 10943, 10947
10949	↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into df-an
10950	→𝜑→⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10951	→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜑↗→𝜑→⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬¬𝜑] into ax-1
10952	→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 10950, 10951
10953	→→¬¬𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜑] into ax-2
10954	→→¬¬𝜑𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 10952, 10953
10955	→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑	Modus ponens notnotr, 10954
10956	→→⋀𝜓⋀𝜒𝜃→𝜑𝜒→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-2
10957	→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10948, 10956
10958	→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗¬¬𝜑] into ax-1
10959	→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10957, 10958
10960	→→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜒] into ax-2
10961	→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10959, 10960
10962	→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10955, 10961
10963	→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃] into id
10964	→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬𝜑] into ax-1
10965	→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10966	→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 10964, 10965
10967	→→⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑⋀𝜓⋀𝜒𝜃] into ax-2
10968	→→⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 10966, 10967
10969	→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜒→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒	Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-2
10970	→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒	Modus ponens 10962, 10969
10971	→→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒	Subs [𝜑↗→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10972	→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒	Modus ponens 10970, 10971
10973	→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑𝜒] into ax-2
10974	→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒	Modus ponens 10972, 10973
10975	→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒	Modus ponens 10964, 10974
10976	→→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒	Subs [𝜑↗→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10977	→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒	Modus ponens 9357, 10976
10978	→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜒→¬¬𝜑¬¬𝜒→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑𝜒, 𝜒↗→¬¬𝜑¬¬𝜒] into ax-2
10979	→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜒→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒	Modus ponens 10977, 10978
10980	→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒	Modus ponens 10975, 10979
10981	→→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10982	→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑	Modus ponens 9363, 10981
10983	→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜒→¬𝜒¬𝜑→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑¬¬𝜒, 𝜒↗→¬𝜒¬𝜑] into ax-2
10984	→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜒→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑	Modus ponens 10982, 10983
10985	→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑	Modus ponens 10980, 10984
10986	→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
10987	→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒	Subs [𝜑↗→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
10988	→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒	Modus ponens 10986, 10987
10989	→→¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜒] into ax-2
10990	→→¬𝜒¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒	Modus ponens 10988, 10989
10991	→→⋀𝜓⋀𝜒𝜃→¬𝜒¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬𝜑] into ax-2
10992	→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10985, 10991
10993	→→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
10994	→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10992, 10993
10995	→→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜒, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
10996	→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10994, 10995
10997	→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10986, 10996
10998	→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into id
10999	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11000	→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10998, 10999
11001	→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into notnotr
11002	→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11003	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11004	→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11002, 11003
11005	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11006	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11004, 11005
11007	→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11001, 11006
11008	→→¬𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11009	→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11000, 11008
11010	→→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11011	→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11009, 11010
11012	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11013	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11011, 11012
11014	→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11015	→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒, 𝜓↗¬𝜒] into ax-1
11016	→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒	Modus ponens 11014, 11015
11017	→→¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒] into ax-2
11018	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒	Modus ponens 11016, 11017
11019	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11020	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11007, 11019
11021	→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11022	→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11020, 11021
11023	→→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11024	→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜒→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11022, 11023
11025	→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11014, 11024
11026	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3
11027	→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜒] into ax-1
11028	→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11026, 11027
11029	→→¬𝜒→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11030	→→¬𝜒→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11028, 11029
11031	→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11025, 11030
11032	→→¬𝜒→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜒, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11033	→→¬𝜒→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11031, 11032
11034	→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10997, 11033
11035	→→¬𝜒¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3
11036	→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Modus ponens 11034, 11035
11037	→↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into biimp
11038	→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10949, 11037
11039	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-1
11040	→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Modus ponens 11036, 11039
11041	→→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒	Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11042	→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒	Modus ponens 11040, 11041
11043	→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒	Modus ponens 11038, 11042
11044	→↔⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into bicom1
11045	↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 10949, 11044
11046	→↔¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into biimp
11047	→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 11045, 11046
11048	→→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒	Subs [𝜑↗→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11049	→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒	Modus ponens 11043, 11048
11050	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜒→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-2
11051	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Modus ponens 11049, 11050
11052	→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into pm3.2im
11053	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒, 𝜓↗𝜑] into ax-1
11054	→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒	Modus ponens 11036, 11053
11055	→→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜒→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒	Subs [𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11056	→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒	Modus ponens 11054, 11055
11057	→→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒	Subs [𝜑↗→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11058	→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒	Modus ponens 11056, 11057
11059	→→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜒→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜒	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→𝜑𝜒] into ax-2
11060	→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜒	Modus ponens 11058, 11059
11061	→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜑↗→𝜑→⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
11062	→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 10950, 11061
11063	→→𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑→→𝜑𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜓↗𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜑] into ax-2
11064	→→𝜑𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 11062, 11063
11065	→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1
11066	→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10957, 11065
11067	→→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜒→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜒] into ax-2
11068	→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11066, 11067
11069	→𝜑→⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 10950, 11068
11070	↔⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into df-an
11071	→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃] into notnotr
11072	→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1
11073	→→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11074	→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 11072, 11073
11075	→→¬¬⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑⋀𝜓⋀𝜒𝜃] into ax-2
11076	→→¬¬⋀𝜓⋀𝜒𝜃⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 11074, 11075
11077	→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃	Modus ponens 11071, 11076
11078	→→𝜑→⋀𝜓⋀𝜒𝜃𝜒→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒	Subs [𝜓↗⋀𝜓⋀𝜒𝜃] into ax-2
11079	→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒	Modus ponens 11069, 11078
11080	→→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒	Subs [𝜑↗→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11081	→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒	Modus ponens 11079, 11080
11082	→→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜒→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒	Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑𝜒] into ax-2
11083	→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒	Modus ponens 11081, 11082
11084	→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒	Modus ponens 11077, 11083
11085	→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11086	→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜑↗→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗𝜑] into ax-1
11087	→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 11085, 11086
11088	→→𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→→𝜑𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑	Subs [𝜓↗𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜑] into ax-2
11089	→→𝜑𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑	Modus ponens 11087, 11088
11090	→→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜒→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-2
11091	→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11084, 11090
11092	→→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗𝜑] into ax-1
11093	→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11091, 11092
11094	→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜒] into ax-2
11095	→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11093, 11094
11096	→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11085, 11095
11097	→→𝜒¬¬𝜒→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒	Subs [𝜑↗→𝜒¬¬𝜒, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11098	→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒	Modus ponens 9172, 11097
11099	→→¬¬⋀𝜓⋀𝜒𝜃→𝜒¬¬𝜒→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒	Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜒, 𝜒↗¬¬𝜒] into ax-2
11100	→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒	Modus ponens 11098, 11099
11101	→→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒	Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒, 𝜓↗𝜑] into ax-1
11102	→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒	Modus ponens 11100, 11101
11103	→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜒→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒	Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜒, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒] into ax-2
11104	→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜒→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒	Modus ponens 11102, 11103
11105	→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒	Modus ponens 11096, 11104
11106	→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-3
11107	→→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1
11108	→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃	Modus ponens 11106, 11107
11109	→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→¬𝜒¬⋀𝜓⋀𝜒𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃	Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒, 𝜒↗→¬𝜒¬⋀𝜓⋀𝜒𝜃] into ax-2
11110	→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜒→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃	Modus ponens 11108, 11109
11111	→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃	Modus ponens 11105, 11110
11112	→→𝜑→¬𝜒¬⋀𝜓⋀𝜒𝜃→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜓↗¬𝜒, 𝜒↗¬⋀𝜓⋀𝜒𝜃] into ax-2
11113	→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11111, 11112
11114	→→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11115	→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11113, 11114
11116	→→¬𝜒→→𝜑¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬𝜒, 𝜒↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11117	→→¬𝜒→𝜑¬𝜒→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11115, 11116
11118	→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 9465, 11117
11119	→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into id
11120	→→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11121	→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11119, 11120
11122	→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into notnotr
11123	→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11124	→→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11125	→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11123, 11124
11126	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11127	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11125, 11126
11128	→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11122, 11127
11129	→→¬𝜒→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11130	→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11121, 11129
11131	→→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11132	→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11130, 11131
11133	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11134	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11132, 11133
11135	→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11136	→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒	Subs [𝜑↗→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒, 𝜓↗¬𝜒] into ax-1
11137	→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒	Modus ponens 11135, 11136
11138	→→¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒] into ax-2
11139	→→¬𝜒¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒	Modus ponens 11137, 11138
11140	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11141	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11128, 11140
11142	→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11143	→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11141, 11142
11144	→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11145	→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜒→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11143, 11144
11146	→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11135, 11145
11147	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3
11148	→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜒] into ax-1
11149	→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11147, 11148
11150	→→¬𝜒→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11151	→→¬𝜒→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11149, 11150
11152	→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11146, 11151
11153	→→¬𝜒→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜒, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11154	→→¬𝜒→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11152, 11153
11155	→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11118, 11154
11156	→→¬𝜒¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3
11157	→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11155, 11156
11158	→↔⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into biimp
11159	→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11070, 11158
11160	→→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1
11161	→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11157, 11160
11162	→→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜒→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11163	→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11161, 11162
11164	→⋀𝜑⋀𝜓⋀𝜒𝜃𝜒	Modus ponens 11159, 11163	simprrl
11165	→⋀𝜒𝜃𝜃	Subs [𝜑↗𝜒, 𝜓↗𝜃] into simpr
11166	→𝜃→𝜓𝜃	Subs [𝜑↗𝜃] into ax-1
11167	→→𝜃→𝜓𝜃→⋀𝜒𝜃→𝜃→𝜓𝜃	Subs [𝜑↗→𝜃→𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11168	→⋀𝜒𝜃→𝜃→𝜓𝜃	Modus ponens 11166, 11167
11169	→→⋀𝜒𝜃→𝜃→𝜓𝜃→→⋀𝜒𝜃𝜃→⋀𝜒𝜃→𝜓𝜃	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗→𝜓𝜃] into ax-2
11170	→→⋀𝜒𝜃𝜃→⋀𝜒𝜃→𝜓𝜃	Modus ponens 11168, 11169
11171	→⋀𝜒𝜃→𝜓𝜃	Modus ponens 11165, 11170
11172	→→⋀𝜒𝜃→𝜓𝜃→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃	Subs [𝜑↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11173	→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃	Modus ponens 11171, 11172
11174	→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃	Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃, 𝜓↗¬¬𝜓] into ax-1
11175	→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃	Modus ponens 11173, 11174
11176	→→¬¬𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜃	Subs [𝜑↗¬¬𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜃] into ax-2
11177	→→¬¬𝜓→⋀𝜒𝜃𝜓→¬¬𝜓→⋀𝜒𝜃𝜃	Modus ponens 11175, 11176
11178	→¬¬𝜓→⋀𝜒𝜃𝜃	Modus ponens 10734, 11177
11179	→→¬¬𝜓→⋀𝜒𝜃𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃	Subs [𝜑↗¬¬𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11180	→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃	Modus ponens 11178, 11179
11181	→→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃	Subs [𝜑↗→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11182	→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃	Modus ponens 11180, 11181
11183	→→⋀𝜒𝜃→→¬¬𝜓⋀𝜒𝜃→¬¬𝜓𝜃→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜃	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜓𝜃] into ax-2
11184	→→⋀𝜒𝜃→¬¬𝜓⋀𝜒𝜃→⋀𝜒𝜃→¬¬𝜓𝜃	Modus ponens 11182, 11183
11185	→⋀𝜒𝜃→¬¬𝜓𝜃	Modus ponens 10743, 11184
11186	→𝜃¬¬𝜃	Subs [𝜑↗𝜃] into notnot
11187	→→𝜃¬¬𝜃→¬¬𝜓→𝜃¬¬𝜃	Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬𝜓] into ax-1
11188	→¬¬𝜓→𝜃¬¬𝜃	Modus ponens 11186, 11187
11189	→→¬¬𝜓→𝜃¬¬𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11190	→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃	Modus ponens 11188, 11189
11191	→→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃	Subs [𝜑↗→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11192	→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃	Modus ponens 11190, 11191
11193	→→⋀𝜒𝜃→→¬¬𝜓𝜃→¬¬𝜓¬¬𝜃→→⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→¬¬𝜓¬¬𝜃	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓𝜃, 𝜒↗→¬¬𝜓¬¬𝜃] into ax-2
11194	→→⋀𝜒𝜃→¬¬𝜓𝜃→⋀𝜒𝜃→¬¬𝜓¬¬𝜃	Modus ponens 11192, 11193
11195	→⋀𝜒𝜃→¬¬𝜓¬¬𝜃	Modus ponens 11185, 11194
11196	→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜃] into ax-3
11197	→→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓, 𝜓↗⋀𝜒𝜃] into ax-1
11198	→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓	Modus ponens 11196, 11197
11199	→→⋀𝜒𝜃→→¬¬𝜓¬¬𝜃→¬𝜃¬𝜓→→⋀𝜒𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→¬𝜃¬𝜓	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→¬¬𝜓¬¬𝜃, 𝜒↗→¬𝜃¬𝜓] into ax-2
11200	→→⋀𝜒𝜃→¬¬𝜓¬¬𝜃→⋀𝜒𝜃→¬𝜃¬𝜓	Modus ponens 11198, 11199
11201	→⋀𝜒𝜃→¬𝜃¬𝜓	Modus ponens 11195, 11200
11202	→¬𝜃¬𝜃	Subs [𝜑↗¬𝜃] into id
11203	→¬𝜃→⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11204	→→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃	Subs [𝜑↗→¬𝜃→⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11205	→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃	Modus ponens 11203, 11204
11206	→→¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→⋀𝜒𝜃¬𝜃] into ax-2
11207	→→¬𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜃	Modus ponens 11205, 11206
11208	→→⋀𝜒𝜃→¬𝜃¬𝜓→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬𝜓] into ax-2
11209	→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓	Modus ponens 11201, 11208
11210	→→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11211	→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓	Modus ponens 11209, 11210
11212	→→¬𝜃→→⋀𝜒𝜃¬𝜃→⋀𝜒𝜃¬𝜓→→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜒𝜃¬𝜃, 𝜒↗→⋀𝜒𝜃¬𝜓] into ax-2
11213	→→¬𝜃→⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜒𝜃¬𝜓	Modus ponens 11211, 11212
11214	→¬𝜃→⋀𝜒𝜃¬𝜓	Modus ponens 11203, 11213
11215	→→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11216	→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 10777, 11215
11217	→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11218	→→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
11219	→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Modus ponens 11217, 11218
11220	→→¬¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜃¬→⋀𝜒𝜃¬𝜓] into ax-2
11221	→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Modus ponens 11219, 11220
11222	→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Modus ponens 10780, 11221
11223	→→¬𝜃→¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
11224	→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Modus ponens 11216, 11223
11225	→→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
11226	→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Modus ponens 11224, 11225
11227	→→¬¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗→¬𝜃¬→⋀𝜒𝜃¬𝜓, 𝜒↗→¬𝜃¬→⋀𝜒𝜃¬𝜓] into ax-2
11228	→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓	Modus ponens 11226, 11227
11229	→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→⋀𝜒𝜃¬𝜓] into ax-1
11230	→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃	Subs [𝜑↗→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃, 𝜓↗¬𝜃] into ax-1
11231	→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃	Modus ponens 11229, 11230
11232	→→¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃] into ax-2
11233	→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃	Modus ponens 11231, 11232
11234	→→¬¬¬→⋀𝜒𝜃¬𝜓→¬𝜃¬→⋀𝜒𝜃¬𝜓→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃, 𝜒↗¬→⋀𝜒𝜃¬𝜓] into ax-2
11235	→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 11222, 11234
11236	→→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11237	→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 11235, 11236
11238	→→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃, 𝜒↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓] into ax-2
11239	→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬𝜃→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 11237, 11238
11240	→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓	Modus ponens 11229, 11239
11241	→→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓, 𝜓↗¬𝜃] into ax-1
11242	→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 10805, 11241
11243	→→¬𝜃→→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓] into ax-2
11244	→→¬𝜃→¬¬¬→⋀𝜒𝜃¬𝜓¬→⋀𝜒𝜃¬𝜓→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 11242, 11243
11245	→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 11240, 11244
11246	→→¬𝜃→→⋀𝜒𝜃¬𝜓¬¬→⋀𝜒𝜃¬𝜓→→¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃¬¬→⋀𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜒𝜃¬𝜓, 𝜒↗¬¬→⋀𝜒𝜃¬𝜓] into ax-2
11247	→→¬𝜃→⋀𝜒𝜃¬𝜓→¬𝜃¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 11245, 11246
11248	→¬𝜃¬¬→⋀𝜒𝜃¬𝜓	Modus ponens 11214, 11247
11249	→→¬𝜃¬¬→⋀𝜒𝜃¬𝜓→¬→⋀𝜒𝜃¬𝜓𝜃	Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-3
11250	→¬→⋀𝜒𝜃¬𝜓𝜃	Modus ponens 11248, 11249
11251	→→¬→⋀𝜒𝜃¬𝜓𝜃→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜃, 𝜓↗⋀⋀𝜒𝜃𝜓] into ax-1
11252	→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃	Modus ponens 11250, 11251
11253	→→⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃	Subs [𝜑↗⋀⋀𝜒𝜃𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗𝜃] into ax-2
11254	→→⋀⋀𝜒𝜃𝜓¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃	Modus ponens 11252, 11253
11255	→⋀⋀𝜒𝜃𝜓𝜃	Modus ponens 10817, 11254
11256	→→⋀⋀𝜒𝜃𝜓𝜃→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃	Subs [𝜑↗→⋀⋀𝜒𝜃𝜓𝜃, 𝜓↗¬→⋀𝜒𝜃¬𝜓] into ax-1
11257	→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃	Modus ponens 11255, 11256
11258	→→¬→⋀𝜒𝜃¬𝜓→⋀⋀𝜒𝜃𝜓𝜃→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃	Subs [𝜑↗¬→⋀𝜒𝜃¬𝜓, 𝜓↗⋀⋀𝜒𝜃𝜓, 𝜒↗𝜃] into ax-2
11259	→→¬→⋀𝜒𝜃¬𝜓⋀⋀𝜒𝜃𝜓→¬→⋀𝜒𝜃¬𝜓𝜃	Modus ponens 11257, 11258
11260	→→¬→⋀𝜒𝜃¬𝜓𝜃→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃	Subs [𝜑↗→¬→⋀𝜒𝜃¬𝜓𝜃] into ax-1
11261	→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃	Modus ponens 11250, 11260
11262	→→𝜓→¬→⋀𝜒𝜃¬𝜓𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃	Subs [𝜑↗𝜓, 𝜓↗¬→⋀𝜒𝜃¬𝜓, 𝜒↗𝜃] into ax-2
11263	→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃	Modus ponens 11261, 11262
11264	→→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃	Subs [𝜑↗→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃, 𝜓↗⋀𝜒𝜃] into ax-1
11265	→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃	Modus ponens 11263, 11264
11266	→→⋀𝜒𝜃→→𝜓¬→⋀𝜒𝜃¬𝜓→𝜓𝜃→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜃	Subs [𝜑↗⋀𝜒𝜃, 𝜓↗→𝜓¬→⋀𝜒𝜃¬𝜓, 𝜒↗→𝜓𝜃] into ax-2
11267	→→⋀𝜒𝜃→𝜓¬→⋀𝜒𝜃¬𝜓→⋀𝜒𝜃→𝜓𝜃	Modus ponens 11265, 11266
11268	→→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃	Subs [𝜑↗→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃] into ax-1
11269	→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃	Modus ponens 11173, 11268
11270	→→𝜓→→⋀𝜒𝜃𝜓→⋀𝜒𝜃𝜃→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜃	Subs [𝜑↗𝜓, 𝜓↗→⋀𝜒𝜃𝜓, 𝜒↗→⋀𝜒𝜃𝜃] into ax-2
11271	→→𝜓→⋀𝜒𝜃𝜓→𝜓→⋀𝜒𝜃𝜃	Modus ponens 11269, 11270
11272	→𝜓→⋀𝜒𝜃𝜃	Modus ponens 10729, 11271
11273	→→𝜓→⋀𝜒𝜃𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃	Subs [𝜑↗𝜓, 𝜓↗⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11274	→→𝜓⋀𝜒𝜃→𝜓𝜃	Modus ponens 11272, 11273
11275	→→→𝜓⋀𝜒𝜃→𝜓𝜃→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃	Subs [𝜑↗→→𝜓⋀𝜒𝜃→𝜓𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
11276	→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃	Modus ponens 11274, 11275
11277	→→¬¬⋀𝜒𝜃→→𝜓⋀𝜒𝜃→𝜓𝜃→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜃	Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗→𝜓⋀𝜒𝜃, 𝜒↗→𝜓𝜃] into ax-2
11278	→→¬¬⋀𝜒𝜃→𝜓⋀𝜒𝜃→¬¬⋀𝜒𝜃→𝜓𝜃	Modus ponens 11276, 11277
11279	→¬¬⋀𝜒𝜃→𝜓𝜃	Modus ponens 10856, 11278
11280	→→¬¬⋀𝜒𝜃→𝜓𝜃→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃	Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11281	→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃	Modus ponens 11279, 11280
11282	→→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃	Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃] into ax-1
11283	→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃	Modus ponens 11281, 11282
11284	→→𝜓→→¬¬⋀𝜒𝜃𝜓→¬¬⋀𝜒𝜃𝜃→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜃	Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜓, 𝜒↗→¬¬⋀𝜒𝜃𝜃] into ax-2
11285	→→𝜓→¬¬⋀𝜒𝜃𝜓→𝜓→¬¬⋀𝜒𝜃𝜃	Modus ponens 11283, 11284
11286	→𝜓→¬¬⋀𝜒𝜃𝜃	Modus ponens 10864, 11285
11287	→→𝜃¬¬𝜃→¬¬⋀𝜒𝜃→𝜃¬¬𝜃	Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬⋀𝜒𝜃] into ax-1
11288	→¬¬⋀𝜒𝜃→𝜃¬¬𝜃	Modus ponens 11186, 11287
11289	→→¬¬⋀𝜒𝜃→𝜃¬¬𝜃→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃	Subs [𝜑↗¬¬⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11290	→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃	Modus ponens 11288, 11289
11291	→→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃	Subs [𝜑↗→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃] into ax-1
11292	→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃	Modus ponens 11290, 11291
11293	→→𝜓→→¬¬⋀𝜒𝜃𝜃→¬¬⋀𝜒𝜃¬¬𝜃→→𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→¬¬⋀𝜒𝜃¬¬𝜃	Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃𝜃, 𝜒↗→¬¬⋀𝜒𝜃¬¬𝜃] into ax-2
11294	→→𝜓→¬¬⋀𝜒𝜃𝜃→𝜓→¬¬⋀𝜒𝜃¬¬𝜃	Modus ponens 11292, 11293
11295	→𝜓→¬¬⋀𝜒𝜃¬¬𝜃	Modus ponens 11286, 11294
11296	→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃	Subs [𝜑↗¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-3
11297	→→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃	Subs [𝜑↗→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃] into ax-1
11298	→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃	Modus ponens 11296, 11297
11299	→→𝜓→→¬¬⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜒𝜃→→𝜓→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→¬𝜃¬⋀𝜒𝜃	Subs [𝜑↗𝜓, 𝜓↗→¬¬⋀𝜒𝜃¬¬𝜃, 𝜒↗→¬𝜃¬⋀𝜒𝜃] into ax-2
11300	→→𝜓→¬¬⋀𝜒𝜃¬¬𝜃→𝜓→¬𝜃¬⋀𝜒𝜃	Modus ponens 11298, 11299
11301	→𝜓→¬𝜃¬⋀𝜒𝜃	Modus ponens 11295, 11300
11302	→¬𝜃→𝜓¬𝜃	Subs [𝜑↗¬𝜃] into ax-1
11303	→→¬𝜃→𝜓¬𝜃→¬𝜃→¬𝜃→𝜓¬𝜃	Subs [𝜑↗→¬𝜃→𝜓¬𝜃, 𝜓↗¬𝜃] into ax-1
11304	→¬𝜃→¬𝜃→𝜓¬𝜃	Modus ponens 11302, 11303
11305	→→¬𝜃→¬𝜃→𝜓¬𝜃→→¬𝜃¬𝜃→¬𝜃→𝜓¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→𝜓¬𝜃] into ax-2
11306	→→¬𝜃¬𝜃→¬𝜃→𝜓¬𝜃	Modus ponens 11304, 11305
11307	→→𝜓→¬𝜃¬⋀𝜒𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃	Subs [𝜑↗𝜓, 𝜓↗¬𝜃, 𝜒↗¬⋀𝜒𝜃] into ax-2
11308	→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃	Modus ponens 11301, 11307
11309	→→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11310	→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃	Modus ponens 11308, 11309
11311	→→¬𝜃→→𝜓¬𝜃→𝜓¬⋀𝜒𝜃→→¬𝜃→𝜓¬𝜃→¬𝜃→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→𝜓¬𝜃, 𝜒↗→𝜓¬⋀𝜒𝜃] into ax-2
11312	→→¬𝜃→𝜓¬𝜃→¬𝜃→𝜓¬⋀𝜒𝜃	Modus ponens 11310, 11311
11313	→¬𝜃→𝜓¬⋀𝜒𝜃	Modus ponens 11302, 11312
11314	→→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11315	→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10898, 11314
11316	→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11317	→→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
11318	→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11316, 11317
11319	→→¬¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
11320	→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11318, 11319
11321	→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 10901, 11320
11322	→→¬𝜃→¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
11323	→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11315, 11322
11324	→→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
11325	→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11323, 11324
11326	→→¬¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗→¬𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
11327	→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11325, 11326
11328	→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→𝜓¬⋀𝜒𝜃] into ax-1
11329	→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃	Subs [𝜑↗→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11330	→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃	Modus ponens 11328, 11329
11331	→→¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃] into ax-2
11332	→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃	Modus ponens 11330, 11331
11333	→→¬¬¬→𝜓¬⋀𝜒𝜃→¬𝜃¬→𝜓¬⋀𝜒𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬→𝜓¬⋀𝜒𝜃] into ax-2
11334	→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11321, 11333
11335	→→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11336	→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11334, 11335
11337	→→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃, 𝜒↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃] into ax-2
11338	→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11336, 11337
11339	→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃	Modus ponens 11328, 11338
11340	→→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11341	→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 10926, 11340
11342	→→¬𝜃→→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃, 𝜒↗→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃] into ax-2
11343	→→¬𝜃→¬¬¬→𝜓¬⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 11341, 11342
11344	→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 11339, 11343
11345	→→¬𝜃→→𝜓¬⋀𝜒𝜃¬¬→𝜓¬⋀𝜒𝜃→→¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃¬¬→𝜓¬⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→𝜓¬⋀𝜒𝜃, 𝜒↗¬¬→𝜓¬⋀𝜒𝜃] into ax-2
11346	→→¬𝜃→𝜓¬⋀𝜒𝜃→¬𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 11344, 11345
11347	→¬𝜃¬¬→𝜓¬⋀𝜒𝜃	Modus ponens 11313, 11346
11348	→→¬𝜃¬¬→𝜓¬⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃	Subs [𝜑↗𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃] into ax-3
11349	→¬→𝜓¬⋀𝜒𝜃𝜃	Modus ponens 11347, 11348
11350	→→¬→𝜓¬⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃	Subs [𝜑↗→¬→𝜓¬⋀𝜒𝜃𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11351	→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃	Modus ponens 11349, 11350
11352	→→⋀𝜓⋀𝜒𝜃→¬→𝜓¬⋀𝜒𝜃𝜃→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜓¬⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11353	→→⋀𝜓⋀𝜒𝜃¬→𝜓¬⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11351, 11352
11354	→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 10938, 11353
11355	→𝜃→𝜑𝜃	Subs [𝜑↗𝜃, 𝜓↗𝜑] into ax-1
11356	→→𝜃→𝜑𝜃→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃	Subs [𝜑↗→𝜃→𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11357	→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃	Modus ponens 11355, 11356
11358	→→⋀𝜓⋀𝜒𝜃→𝜃→𝜑𝜃→→⋀𝜓⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→𝜑𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗→𝜑𝜃] into ax-2
11359	→→⋀𝜓⋀𝜒𝜃𝜃→⋀𝜓⋀𝜒𝜃→𝜑𝜃	Modus ponens 11357, 11358
11360	→⋀𝜓⋀𝜒𝜃→𝜑𝜃	Modus ponens 11354, 11359
11361	→→⋀𝜓⋀𝜒𝜃→𝜑𝜃→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜃] into ax-2
11362	→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11360, 11361
11363	→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗¬¬𝜑] into ax-1
11364	→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11362, 11363
11365	→→¬¬𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗¬¬𝜑, 𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜃] into ax-2
11366	→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜑→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11364, 11365
11367	→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 10955, 11366
11368	→→¬¬𝜑→⋀𝜓⋀𝜒𝜃𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃	Subs [𝜑↗¬¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11369	→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃	Modus ponens 11367, 11368
11370	→→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃	Subs [𝜑↗→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11371	→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃	Modus ponens 11369, 11370
11372	→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→¬¬𝜑𝜃] into ax-2
11373	→→⋀𝜓⋀𝜒𝜃→¬¬𝜑⋀𝜓⋀𝜒𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃	Modus ponens 11371, 11372
11374	→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃	Modus ponens 10964, 11373
11375	→→𝜃¬¬𝜃→¬¬𝜑→𝜃¬¬𝜃	Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬𝜑] into ax-1
11376	→¬¬𝜑→𝜃¬¬𝜃	Modus ponens 11186, 11375
11377	→→¬¬𝜑→𝜃¬¬𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃	Subs [𝜑↗¬¬𝜑, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11378	→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃	Modus ponens 11376, 11377
11379	→→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃	Subs [𝜑↗→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11380	→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃	Modus ponens 11378, 11379
11381	→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑𝜃→¬¬𝜑¬¬𝜃→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑𝜃, 𝜒↗→¬¬𝜑¬¬𝜃] into ax-2
11382	→→⋀𝜓⋀𝜒𝜃→¬¬𝜑𝜃→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃	Modus ponens 11380, 11381
11383	→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃	Modus ponens 11374, 11382
11384	→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜃] into ax-3
11385	→→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑	Subs [𝜑↗→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11386	→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑	Modus ponens 11384, 11385
11387	→→⋀𝜓⋀𝜒𝜃→→¬¬𝜑¬¬𝜃→¬𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→¬¬𝜑¬¬𝜃, 𝜒↗→¬𝜃¬𝜑] into ax-2
11388	→→⋀𝜓⋀𝜒𝜃→¬¬𝜑¬¬𝜃→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑	Modus ponens 11386, 11387
11389	→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑	Modus ponens 11383, 11388
11390	→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11391	→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃	Subs [𝜑↗→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11392	→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃	Modus ponens 11390, 11391
11393	→→¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜃] into ax-2
11394	→→¬𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃	Modus ponens 11392, 11393
11395	→→⋀𝜓⋀𝜒𝜃→¬𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬𝜑] into ax-2
11396	→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11389, 11395
11397	→→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11398	→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11396, 11397
11399	→→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜃, 𝜒↗→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11400	→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11398, 11399
11401	→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11390, 11400
11402	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11403	→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 10998, 11402
11404	→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11405	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11406	→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11404, 11405
11407	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11408	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11406, 11407
11409	→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11001, 11408
11410	→→¬𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11411	→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11403, 11410
11412	→→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11413	→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11411, 11412
11414	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11415	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11413, 11414
11416	→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11417	→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃	Subs [𝜑↗→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃, 𝜓↗¬𝜃] into ax-1
11418	→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃	Modus ponens 11416, 11417
11419	→→¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃] into ax-2
11420	→→¬𝜃¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃	Modus ponens 11418, 11419
11421	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃, 𝜒↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11422	→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11409, 11421
11423	→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11424	→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11422, 11423
11425	→→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃, 𝜒↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11426	→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬𝜃→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11424, 11425
11427	→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11416, 11426
11428	→→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗¬𝜃] into ax-1
11429	→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11026, 11428
11430	→→¬𝜃→→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11431	→→¬𝜃→¬¬¬→⋀𝜓⋀𝜒𝜃¬𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11429, 11430
11432	→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11427, 11431
11433	→→¬𝜃→→⋀𝜓⋀𝜒𝜃¬𝜑¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜃, 𝜓↗→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗¬¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-2
11434	→→¬𝜃→⋀𝜓⋀𝜒𝜃¬𝜑→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11432, 11433
11435	→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑	Modus ponens 11401, 11434
11436	→→¬𝜃¬¬→⋀𝜓⋀𝜒𝜃¬𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Subs [𝜑↗𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-3
11437	→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Modus ponens 11435, 11436
11438	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑] into ax-1
11439	→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Modus ponens 11437, 11438
11440	→→⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃	Subs [𝜑↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗𝜃] into ax-2
11441	→→⋀⋀𝜓⋀𝜒𝜃𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃	Modus ponens 11439, 11440
11442	→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃	Modus ponens 11038, 11441
11443	→→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃	Subs [𝜑↗→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃, 𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑] into ax-1
11444	→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃	Modus ponens 11442, 11443
11445	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀⋀𝜓⋀𝜒𝜃𝜑𝜃→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Subs [𝜑↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜓↗⋀⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗𝜃] into ax-2
11446	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑⋀⋀𝜓⋀𝜒𝜃𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Modus ponens 11444, 11445
11447	→→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Subs [𝜑↗→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃, 𝜓↗𝜑] into ax-1
11448	→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃	Modus ponens 11437, 11447
11449	→→𝜑→¬→⋀𝜓⋀𝜒𝜃¬𝜑𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃	Subs [𝜓↗¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗𝜃] into ax-2
11450	→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃	Modus ponens 11448, 11449
11451	→→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃	Subs [𝜑↗→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃, 𝜓↗⋀𝜓⋀𝜒𝜃] into ax-1
11452	→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃	Modus ponens 11450, 11451
11453	→→⋀𝜓⋀𝜒𝜃→→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→𝜑𝜃→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜃	Subs [𝜑↗⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑, 𝜒↗→𝜑𝜃] into ax-2
11454	→→⋀𝜓⋀𝜒𝜃→𝜑¬→⋀𝜓⋀𝜒𝜃¬𝜑→⋀𝜓⋀𝜒𝜃→𝜑𝜃	Modus ponens 11452, 11453
11455	→→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗𝜑] into ax-1
11456	→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11362, 11455
11457	→→𝜑→→⋀𝜓⋀𝜒𝜃𝜑→⋀𝜓⋀𝜒𝜃𝜃→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜓↗→⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→⋀𝜓⋀𝜒𝜃𝜃] into ax-2
11458	→→𝜑→⋀𝜓⋀𝜒𝜃𝜑→𝜑→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11456, 11457
11459	→𝜑→⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 10950, 11458
11460	→→𝜑→⋀𝜓⋀𝜒𝜃𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃	Subs [𝜓↗⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11461	→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃	Modus ponens 11459, 11460
11462	→→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃	Subs [𝜑↗→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11463	→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃	Modus ponens 11461, 11462
11464	→→¬¬⋀𝜓⋀𝜒𝜃→→𝜑⋀𝜓⋀𝜒𝜃→𝜑𝜃→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃	Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗→𝜑⋀𝜓⋀𝜒𝜃, 𝜒↗→𝜑𝜃] into ax-2
11465	→→¬¬⋀𝜓⋀𝜒𝜃→𝜑⋀𝜓⋀𝜒𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃	Modus ponens 11463, 11464
11466	→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃	Modus ponens 11077, 11465
11467	→→¬¬⋀𝜓⋀𝜒𝜃→𝜑𝜃→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑, 𝜒↗𝜃] into ax-2
11468	→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11466, 11467
11469	→→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗𝜑] into ax-1
11470	→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11468, 11469
11471	→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜑, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃𝜃] into ax-2
11472	→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜑→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11470, 11471
11473	→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11085, 11472
11474	→→𝜃¬¬𝜃→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃	Subs [𝜑↗→𝜃¬¬𝜃, 𝜓↗¬¬⋀𝜓⋀𝜒𝜃] into ax-1
11475	→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃	Modus ponens 11186, 11474
11476	→→¬¬⋀𝜓⋀𝜒𝜃→𝜃¬¬𝜃→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃	Subs [𝜑↗¬¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜃, 𝜒↗¬¬𝜃] into ax-2
11477	→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃	Modus ponens 11475, 11476
11478	→→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃	Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃, 𝜓↗𝜑] into ax-1
11479	→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃	Modus ponens 11477, 11478
11480	→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃𝜃→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃	Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃𝜃, 𝜒↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃] into ax-2
11481	→→𝜑→¬¬⋀𝜓⋀𝜒𝜃𝜃→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃	Modus ponens 11479, 11480
11482	→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃	Modus ponens 11473, 11481
11483	→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-3
11484	→→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃, 𝜓↗𝜑] into ax-1
11485	→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃	Modus ponens 11483, 11484
11486	→→𝜑→→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→¬𝜃¬⋀𝜓⋀𝜒𝜃→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃	Subs [𝜓↗→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃, 𝜒↗→¬𝜃¬⋀𝜓⋀𝜒𝜃] into ax-2
11487	→→𝜑→¬¬⋀𝜓⋀𝜒𝜃¬¬𝜃→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃	Modus ponens 11485, 11486
11488	→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃	Modus ponens 11482, 11487
11489	→¬𝜃→𝜑¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗𝜑] into ax-1
11490	→→¬𝜃→𝜑¬𝜃→¬𝜃→¬𝜃→𝜑¬𝜃	Subs [𝜑↗→¬𝜃→𝜑¬𝜃, 𝜓↗¬𝜃] into ax-1
11491	→¬𝜃→¬𝜃→𝜑¬𝜃	Modus ponens 11489, 11490
11492	→→¬𝜃→¬𝜃→𝜑¬𝜃→→¬𝜃¬𝜃→¬𝜃→𝜑¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→𝜑¬𝜃] into ax-2
11493	→→¬𝜃¬𝜃→¬𝜃→𝜑¬𝜃	Modus ponens 11491, 11492
11494	→→𝜑→¬𝜃¬⋀𝜓⋀𝜒𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜓↗¬𝜃, 𝜒↗¬⋀𝜓⋀𝜒𝜃] into ax-2
11495	→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11488, 11494
11496	→→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11497	→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11495, 11496
11498	→→¬𝜃→→𝜑¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→𝜑¬𝜃→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→𝜑¬𝜃, 𝜒↗→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11499	→→¬𝜃→𝜑¬𝜃→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11497, 11498
11500	→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11489, 11499
11501	→→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11502	→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11119, 11501
11503	→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11504	→→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11505	→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11503, 11504
11506	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11507	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11505, 11506
11508	→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11122, 11507
11509	→→¬𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11510	→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11502, 11509
11511	→→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11512	→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11510, 11511
11513	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11514	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11512, 11513
11515	→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-1
11516	→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃	Subs [𝜑↗→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃, 𝜓↗¬𝜃] into ax-1
11517	→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃	Modus ponens 11515, 11516
11518	→→¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃	Subs [𝜑↗¬𝜃, 𝜓↗¬𝜃, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃] into ax-2
11519	→→¬𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃	Modus ponens 11517, 11518
11520	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃, 𝜒↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11521	→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11508, 11520
11522	→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11523	→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11521, 11522
11524	→→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃, 𝜒↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11525	→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬𝜃→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11523, 11524
11526	→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11515, 11525
11527	→→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜓↗¬𝜃] into ax-1
11528	→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11147, 11527
11529	→→¬𝜃→→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11530	→→¬𝜃→¬¬¬→𝜑¬⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11528, 11529
11531	→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11526, 11530
11532	→→¬𝜃→→𝜑¬⋀𝜓⋀𝜒𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Subs [𝜑↗¬𝜃, 𝜓↗→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗¬¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-2
11533	→→¬𝜃→𝜑¬⋀𝜓⋀𝜒𝜃→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11531, 11532
11534	→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃	Modus ponens 11500, 11533
11535	→→¬𝜃¬¬→𝜑¬⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃] into ax-3
11536	→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11534, 11535
11537	→→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃, 𝜓↗⋀𝜑⋀𝜓⋀𝜒𝜃] into ax-1
11538	→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11536, 11537
11539	→→⋀𝜑⋀𝜓⋀𝜒𝜃→¬→𝜑¬⋀𝜓⋀𝜒𝜃𝜃→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃	Subs [𝜑↗⋀𝜑⋀𝜓⋀𝜒𝜃, 𝜓↗¬→𝜑¬⋀𝜓⋀𝜒𝜃, 𝜒↗𝜃] into ax-2
11540	→→⋀𝜑⋀𝜓⋀𝜒𝜃¬→𝜑¬⋀𝜓⋀𝜒𝜃→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11538, 11539
11541	→⋀𝜑⋀𝜓⋀𝜒𝜃𝜃	Modus ponens 11159, 11540	simprrr
11542	→𝜑→𝜏𝜑	Subs [𝜓↗𝜏] into ax-1
11543	→→𝜑→𝜏𝜑→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑	Subs [𝜑↗→𝜑→𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11544	→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑	Modus ponens 11542, 11543
11545	→→⋀⋀𝜑𝜓𝜒→𝜑→𝜏𝜑→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜏𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜏𝜑] into ax-2
11546	→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜏𝜑	Modus ponens 11544, 11545
11547	→⋀⋀𝜑𝜓𝜒→𝜏𝜑	Modus ponens simpll, 11546
11548	↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into df-an
11549	→¬¬𝜏𝜏	Subs [𝜑↗𝜏] into notnotr
11550	→𝜏→⋀⋀𝜑𝜓𝜒𝜏	Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11551	→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏	Subs [𝜑↗→𝜏→⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬¬𝜏] into ax-1
11552	→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏	Modus ponens 11550, 11551
11553	→→¬¬𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏	Subs [𝜑↗¬¬𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜏] into ax-2
11554	→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏	Modus ponens 11552, 11553
11555	→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏	Modus ponens 11549, 11554
11556	→→⋀⋀𝜑𝜓𝜒→𝜏𝜑→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏, 𝜒↗𝜑] into ax-2
11557	→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 11547, 11556
11558	→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗¬¬𝜏] into ax-1
11559	→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 11557, 11558
11560	→→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
11561	→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 11559, 11560
11562	→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 11555, 11561
11563	→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬¬𝜏] into ax-1
11564	→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11565	→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒	Modus ponens 11563, 11564
11566	→→⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏⋀⋀𝜑𝜓𝜒] into ax-2
11567	→→⋀⋀𝜑𝜓𝜒⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒	Modus ponens 11565, 11566
11568	→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜑→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑	Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
11569	→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑	Modus ponens 11562, 11568
11570	→→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑	Subs [𝜑↗→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11571	→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑	Modus ponens 11569, 11570
11572	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏𝜑] into ax-2
11573	→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑	Modus ponens 11571, 11572
11574	→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑	Modus ponens 11563, 11573
11575	→→𝜑¬¬𝜑→¬¬𝜏→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜏] into ax-1
11576	→¬¬𝜏→𝜑¬¬𝜑	Modus ponens notnot, 11575
11577	→→¬¬𝜏→𝜑¬¬𝜑→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑	Subs [𝜑↗¬¬𝜏, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
11578	→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑	Modus ponens 11576, 11577
11579	→→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑	Subs [𝜑↗→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11580	→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑	Modus ponens 11578, 11579
11581	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏𝜑, 𝜒↗→¬¬𝜏¬¬𝜑] into ax-2
11582	→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜑→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑	Modus ponens 11580, 11581
11583	→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑	Modus ponens 11574, 11582
11584	→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏	Subs [𝜑↗¬𝜏, 𝜓↗¬𝜑] into ax-3
11585	→→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏	Subs [𝜑↗→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11586	→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏	Modus ponens 11584, 11585
11587	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏¬¬𝜑, 𝜒↗→¬𝜑¬𝜏] into ax-2
11588	→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜑→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏	Modus ponens 11586, 11587
11589	→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏	Modus ponens 11583, 11588
11590	→→⋀⋀𝜑𝜓𝜒→¬𝜑¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜑, 𝜒↗¬𝜏] into ax-2
11591	→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11589, 11590
11592	→→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11593	→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11591, 11592
11594	→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜑, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11595	→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜑→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11593, 11594
11596	→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 9716, 11595
11597	→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into id
11598	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11599	→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11597, 11598
11600	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into notnotr
11601	→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11602	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11603	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11601, 11602
11604	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11605	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11603, 11604
11606	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11600, 11605
11607	→→¬𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11608	→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11599, 11607
11609	→→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11610	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11608, 11609
11611	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11612	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11610, 11611
11613	→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11614	→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1
11615	→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑	Modus ponens 11613, 11614
11616	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑] into ax-2
11617	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑	Modus ponens 11615, 11616
11618	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11619	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11606, 11618
11620	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11621	→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11619, 11620
11622	→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11623	→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11621, 11622
11624	→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11613, 11623
11625	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3
11626	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜑] into ax-1
11627	→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11625, 11626
11628	→→¬𝜑→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11629	→→¬𝜑→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11627, 11628
11630	→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11624, 11629
11631	→→¬𝜑→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11632	→→¬𝜑→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11630, 11631
11633	→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11596, 11632
11634	→→¬𝜑¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Subs [𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3
11635	→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Modus ponens 11633, 11634
11636	→↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into biimp
11637	→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11548, 11636
11638	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into ax-1
11639	→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Modus ponens 11635, 11638
11640	→→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜑] into ax-2
11641	→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑	Modus ponens 11639, 11640
11642	→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑	Modus ponens 11637, 11641
11643	→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜃] into simpl
11644	→↔⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into bicom1
11645	↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏	Modus ponens 11548, 11644
11646	→↔¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into biimp
11647	→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏	Modus ponens 11645, 11646
11648	→→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑	Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11649	→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑	Modus ponens 11642, 11648
11650	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜑→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗𝜑] into ax-2
11651	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Modus ponens 11649, 11650
11652	→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into pm3.2im
11653	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑, 𝜓↗𝜏] into ax-1
11654	→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑	Modus ponens 11635, 11653
11655	→→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜑→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑	Subs [𝜑↗𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜑] into ax-2
11656	→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑	Modus ponens 11654, 11655
11657	→→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑	Subs [𝜑↗→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11658	→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑	Modus ponens 11656, 11657
11659	→→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜑→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→𝜏𝜑] into ax-2
11660	→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜑	Modus ponens 11658, 11659
11661	→𝜏𝜏	Subs [𝜑↗𝜏] into id
11662	→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏	Subs [𝜑↗→𝜏→⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗𝜏] into ax-1
11663	→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏	Modus ponens 11550, 11662
11664	→→𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏→→𝜏𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏	Subs [𝜑↗𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜏] into ax-2
11665	→→𝜏𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜏	Modus ponens 11663, 11664
11666	→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑, 𝜓↗𝜏] into ax-1
11667	→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 11557, 11666
11668	→→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜑→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜑	Subs [𝜑↗𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜑] into ax-2
11669	→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 11667, 11668
11670	→𝜏→⋀⋀𝜑𝜓𝜒𝜑	Modus ponens 11550, 11669
11671	→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏] into ax-1
11672	→→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11673	→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒	Modus ponens 11671, 11672
11674	→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀𝜑𝜓𝜒→𝜏⋀⋀𝜑𝜓𝜒→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏⋀⋀𝜑𝜓𝜒] into ax-2
11675	→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒	Modus ponens 11673, 11674
11676	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒	Modus ponens 11643, 11675
11677	→→𝜏→⋀⋀𝜑𝜓𝜒𝜑→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑	Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜑] into ax-2
11678	→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑	Modus ponens 11670, 11677
11679	→→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑	Subs [𝜑↗→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11680	→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑	Modus ponens 11678, 11679
11681	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜑] into ax-2
11682	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Modus ponens 11680, 11681
11683	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Modus ponens 11676, 11682
11684	→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11685	→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜏] into ax-1
11686	→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 11684, 11685
11687	→→𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜏𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
11688	→→𝜏𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 11686, 11687
11689	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏, 𝜒↗𝜑] into ax-2
11690	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 11683, 11689
11691	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗𝜏] into ax-1
11692	→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 11690, 11691
11693	→→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
11694	→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 11692, 11693
11695	→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 11684, 11694
11696	→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃] into id
11697	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into ax-1
11698	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11699	→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 11697, 11698
11700	→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
11701	→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 11699, 11700
11702	→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
11703	→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Modus ponens 11695, 11702
11704	→→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Subs [𝜑↗→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11705	→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Modus ponens 11703, 11704
11706	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜑] into ax-2
11707	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Modus ponens 11705, 11706
11708	↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into df-an
11709	→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜏] into ax-1
11710	→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 11684, 11709
11711	→→¬¬𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗¬¬𝜏, 𝜓↗𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
11712	→→¬¬𝜏𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 11710, 11711
11713	→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 11549, 11712
11714	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜏] into ax-1
11715	→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 11690, 11714
11716	→→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
11717	→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 11715, 11716
11718	→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 11713, 11717
11719	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜏] into ax-1
11720	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11721	→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 11719, 11720
11722	→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
11723	→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 11721, 11722
11724	→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑	Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
11725	→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑	Modus ponens 11718, 11724
11726	→→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑	Subs [𝜑↗→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11727	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑	Modus ponens 11725, 11726
11728	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏𝜑] into ax-2
11729	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑	Modus ponens 11727, 11728
11730	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑	Modus ponens 11719, 11729
11731	→→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑	Subs [𝜑↗→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11732	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑	Modus ponens 11578, 11731
11733	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜑→¬¬𝜏¬¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏𝜑, 𝜒↗→¬¬𝜏¬¬𝜑] into ax-2
11734	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑	Modus ponens 11732, 11733
11735	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑	Modus ponens 11730, 11734
11736	→→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏	Subs [𝜑↗→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11737	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏	Modus ponens 11584, 11736
11738	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜑→¬𝜑¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏¬¬𝜑, 𝜒↗→¬𝜑¬𝜏] into ax-2
11739	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏	Modus ponens 11737, 11738
11740	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏	Modus ponens 11735, 11739
11741	→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11742	→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜓↗¬𝜑] into ax-1
11743	→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑	Modus ponens 11741, 11742
11744	→→¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑] into ax-2
11745	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑	Modus ponens 11743, 11744
11746	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜑, 𝜒↗¬𝜏] into ax-2
11747	→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11740, 11746
11748	→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11749	→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11747, 11748
11750	→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11751	→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11749, 11750
11752	→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11741, 11751
11753	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into id
11754	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11755	→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11753, 11754
11756	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into notnotr
11757	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11758	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11759	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11757, 11758
11760	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11761	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11759, 11760
11762	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11756, 11761
11763	→→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11764	→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11755, 11763
11765	→→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11766	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11764, 11765
11767	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11768	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11766, 11767
11769	→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11770	→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1
11771	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑	Modus ponens 11769, 11770
11772	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑] into ax-2
11773	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑	Modus ponens 11771, 11772
11774	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11775	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11762, 11774
11776	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11777	→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11775, 11776
11778	→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11779	→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11777, 11778
11780	→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11769, 11779
11781	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3
11782	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜑] into ax-1
11783	→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11781, 11782
11784	→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11785	→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11783, 11784
11786	→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11780, 11785
11787	→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11788	→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11786, 11787
11789	→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11752, 11788
11790	→→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑	Subs [𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3
11791	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑	Modus ponens 11789, 11790
11792	→↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into biimp
11793	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11708, 11792
11794	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
11795	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑	Modus ponens 11791, 11794
11796	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗𝜑] into ax-2
11797	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 11795, 11796
11798	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 11793, 11797	simp-4l
11799	→𝜓→𝜏𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜏] into ax-1
11800	→→𝜓→𝜏𝜓→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓	Subs [𝜑↗→𝜓→𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11801	→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓	Modus ponens 11799, 11800
11802	→→⋀⋀𝜑𝜓𝜒→𝜓→𝜏𝜓→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜏𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜓] into ax-2
11803	→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜏𝜓	Modus ponens 11801, 11802
11804	→⋀⋀𝜑𝜓𝜒→𝜏𝜓	Modus ponens simplr, 11803
11805	→→⋀⋀𝜑𝜓𝜒→𝜏𝜓→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜏, 𝜒↗𝜓] into ax-2
11806	→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 11804, 11805
11807	→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗¬¬𝜏] into ax-1
11808	→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 11806, 11807
11809	→→¬¬𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
11810	→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜏→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 11808, 11809
11811	→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 11555, 11810
11812	→→¬¬𝜏→⋀⋀𝜑𝜓𝜒𝜓→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓	Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
11813	→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓	Modus ponens 11811, 11812
11814	→→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓	Subs [𝜑↗→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11815	→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓	Modus ponens 11813, 11814
11816	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→¬¬𝜏𝜓] into ax-2
11817	→→⋀⋀𝜑𝜓𝜒→¬¬𝜏⋀⋀𝜑𝜓𝜒→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓	Modus ponens 11815, 11816
11818	→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓	Modus ponens 11563, 11817
11819	→→𝜓¬¬𝜓→¬¬𝜏→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜏] into ax-1
11820	→¬¬𝜏→𝜓¬¬𝜓	Modus ponens 448, 11819
11821	→→¬¬𝜏→𝜓¬¬𝜓→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓	Subs [𝜑↗¬¬𝜏, 𝜒↗¬¬𝜓] into ax-2
11822	→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓	Modus ponens 11820, 11821
11823	→→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓	Subs [𝜑↗→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11824	→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓	Modus ponens 11822, 11823
11825	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏𝜓, 𝜒↗→¬¬𝜏¬¬𝜓] into ax-2
11826	→→⋀⋀𝜑𝜓𝜒→¬¬𝜏𝜓→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓	Modus ponens 11824, 11825
11827	→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓	Modus ponens 11818, 11826
11828	→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏	Subs [𝜑↗¬𝜏, 𝜓↗¬𝜓] into ax-3
11829	→→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏	Subs [𝜑↗→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11830	→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏	Modus ponens 11828, 11829
11831	→→⋀⋀𝜑𝜓𝜒→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→¬¬𝜏¬¬𝜓, 𝜒↗→¬𝜓¬𝜏] into ax-2
11832	→→⋀⋀𝜑𝜓𝜒→¬¬𝜏¬¬𝜓→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏	Modus ponens 11830, 11831
11833	→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏	Modus ponens 11827, 11832
11834	→→⋀⋀𝜑𝜓𝜒→¬𝜓¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗¬𝜓, 𝜒↗¬𝜏] into ax-2
11835	→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11833, 11834
11836	→→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11837	→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11835, 11836
11838	→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜓, 𝜒↗→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11839	→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜓→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11837, 11838
11840	→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 9916, 11839
11841	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11842	→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11597, 11841
11843	→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11844	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11845	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11843, 11844
11846	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11847	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11845, 11846
11848	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11600, 11847
11849	→→¬𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11850	→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11842, 11849
11851	→→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11852	→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11850, 11851
11853	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11854	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11852, 11853
11855	→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11856	→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1
11857	→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓	Modus ponens 11855, 11856
11858	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓] into ax-2
11859	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓	Modus ponens 11857, 11858
11860	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11861	→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11848, 11860
11862	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11863	→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11861, 11862
11864	→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓, 𝜒↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11865	→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11863, 11864
11866	→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11855, 11865
11867	→→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗¬𝜓] into ax-1
11868	→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11625, 11867
11869	→→¬𝜓→→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11870	→→¬𝜓→¬¬¬→⋀⋀𝜑𝜓𝜒¬𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11868, 11869
11871	→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11866, 11870
11872	→→¬𝜓→→⋀⋀𝜑𝜓𝜒¬𝜏¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗¬¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-2
11873	→→¬𝜓→⋀⋀𝜑𝜓𝜒¬𝜏→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11871, 11872
11874	→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏	Modus ponens 11840, 11873
11875	→→¬𝜓¬¬→⋀⋀𝜑𝜓𝜒¬𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-3
11876	→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Modus ponens 11874, 11875
11877	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏] into ax-1
11878	→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Modus ponens 11876, 11877
11879	→→⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜓] into ax-2
11880	→→⋀⋀⋀𝜑𝜓𝜒𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓	Modus ponens 11878, 11879
11881	→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓	Modus ponens 11637, 11880
11882	→→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓	Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏] into ax-1
11883	→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓	Modus ponens 11881, 11882
11884	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜏𝜓→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Subs [𝜑↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗𝜓] into ax-2
11885	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Modus ponens 11883, 11884
11886	→→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Subs [𝜑↗→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓, 𝜓↗𝜏] into ax-1
11887	→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓	Modus ponens 11876, 11886
11888	→→𝜏→¬→⋀⋀𝜑𝜓𝜒¬𝜏𝜓→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓	Subs [𝜑↗𝜏, 𝜓↗¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗𝜓] into ax-2
11889	→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓	Modus ponens 11887, 11888
11890	→→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓	Subs [𝜑↗→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11891	→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓	Modus ponens 11889, 11890
11892	→→⋀⋀𝜑𝜓𝜒→→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→𝜏𝜓→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏, 𝜒↗→𝜏𝜓] into ax-2
11893	→→⋀⋀𝜑𝜓𝜒→𝜏¬→⋀⋀𝜑𝜓𝜒¬𝜏→⋀⋀𝜑𝜓𝜒→𝜏𝜓	Modus ponens 11891, 11892
11894	→→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓, 𝜓↗𝜏] into ax-1
11895	→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 11806, 11894
11896	→→𝜏→→⋀⋀𝜑𝜓𝜒𝜏→⋀⋀𝜑𝜓𝜒𝜓→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜓	Subs [𝜑↗𝜏, 𝜓↗→⋀⋀𝜑𝜓𝜒𝜏, 𝜒↗→⋀⋀𝜑𝜓𝜒𝜓] into ax-2
11897	→→𝜏→⋀⋀𝜑𝜓𝜒𝜏→𝜏→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 11895, 11896
11898	→𝜏→⋀⋀𝜑𝜓𝜒𝜓	Modus ponens 11550, 11897
11899	→→𝜏→⋀⋀𝜑𝜓𝜒𝜓→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓	Subs [𝜑↗𝜏, 𝜓↗⋀⋀𝜑𝜓𝜒, 𝜒↗𝜓] into ax-2
11900	→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓	Modus ponens 11898, 11899
11901	→→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓	Subs [𝜑↗→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11902	→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓	Modus ponens 11900, 11901
11903	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀𝜑𝜓𝜒→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜏𝜓] into ax-2
11904	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀𝜑𝜓𝜒→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Modus ponens 11902, 11903
11905	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Modus ponens 11676, 11904
11906	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏, 𝜒↗𝜓] into ax-2
11907	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 11905, 11906
11908	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗𝜏] into ax-1
11909	→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 11907, 11908
11910	→→𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
11911	→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 11909, 11910
11912	→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 11684, 11911
11913	→→𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Subs [𝜑↗𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
11914	→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Modus ponens 11912, 11913
11915	→→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Subs [𝜑↗→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11916	→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Modus ponens 11914, 11915
11917	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜓] into ax-2
11918	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Modus ponens 11916, 11917
11919	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗¬¬𝜏] into ax-1
11920	→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 11907, 11919
11921	→→¬¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗¬¬𝜏, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
11922	→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 11920, 11921
11923	→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 11713, 11922
11924	→→¬¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓	Subs [𝜑↗¬¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
11925	→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓	Modus ponens 11923, 11924
11926	→→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓	Subs [𝜑↗→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11927	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓	Modus ponens 11925, 11926
11928	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜏𝜓] into ax-2
11929	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓	Modus ponens 11927, 11928
11930	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓	Modus ponens 11719, 11929
11931	→→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓	Subs [𝜑↗→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11932	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓	Modus ponens 11822, 11931
11933	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏𝜓→¬¬𝜏¬¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏𝜓, 𝜒↗→¬¬𝜏¬¬𝜓] into ax-2
11934	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓	Modus ponens 11932, 11933
11935	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓	Modus ponens 11930, 11934
11936	→→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏	Subs [𝜑↗→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11937	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏	Modus ponens 11828, 11936
11938	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜏¬¬𝜓→¬𝜓¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜏¬¬𝜓, 𝜒↗→¬𝜓¬𝜏] into ax-2
11939	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜏¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏	Modus ponens 11937, 11938
11940	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏	Modus ponens 11935, 11939
11941	→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
11942	→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜓↗¬𝜓] into ax-1
11943	→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓	Modus ponens 11941, 11942
11944	→→¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓] into ax-2
11945	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓	Modus ponens 11943, 11944
11946	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜓, 𝜒↗¬𝜏] into ax-2
11947	→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11940, 11946
11948	→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11949	→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11947, 11948
11950	→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11951	→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11949, 11950
11952	→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11941, 11951
11953	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11954	→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11753, 11953
11955	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11956	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11957	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11955, 11956
11958	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11959	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11957, 11958
11960	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11756, 11959
11961	→→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11962	→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11954, 11961
11963	→→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11964	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11962, 11963
11965	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11966	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11964, 11965
11967	→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-1
11968	→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1
11969	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓	Modus ponens 11967, 11968
11970	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓] into ax-2
11971	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓	Modus ponens 11969, 11970
11972	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11973	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11960, 11972
11974	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11975	→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11973, 11974
11976	→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11977	→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11975, 11976
11978	→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11967, 11977
11979	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜓↗¬𝜓] into ax-1
11980	→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11781, 11979
11981	→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11982	→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11980, 11981
11983	→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11978, 11982
11984	→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-2
11985	→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11983, 11984
11986	→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏	Modus ponens 11952, 11985
11987	→→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏] into ax-3
11988	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓	Modus ponens 11986, 11987
11989	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
11990	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓	Modus ponens 11988, 11989
11991	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏, 𝜒↗𝜓] into ax-2
11992	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 11990, 11991
11993	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 11793, 11992	simp-4r
11994	→→𝜑→𝜃𝜑→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑	Subs [𝜑↗→𝜑→𝜃𝜑, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
11995	→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑	Modus ponens 9518, 11994
11996	→→⋀⋀𝜑𝜓𝜒→𝜑→𝜃𝜑→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜃𝜑	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜓↗𝜑, 𝜒↗→𝜃𝜑] into ax-2
11997	→→⋀⋀𝜑𝜓𝜒𝜑→⋀⋀𝜑𝜓𝜒→𝜃𝜑	Modus ponens 11995, 11996
11998	→𝜑→𝜂𝜑	Subs [𝜓↗𝜂] into ax-1
11999	→→𝜑→𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑	Subs [𝜑↗→𝜑→𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12000	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑	Modus ponens 11998, 11999
12001	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→𝜂𝜑] into ax-2
12002	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Modus ponens 12000, 12001
12003	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Modus ponens simplll, 12002
12004	↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into df-an
12005	→¬¬𝜂𝜂	Subs [𝜑↗𝜂] into notnotr
12006	→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12007	→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Subs [𝜑↗→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬¬𝜂] into ax-1
12008	→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Modus ponens 12006, 12007
12009	→→¬¬𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Subs [𝜑↗¬¬𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-2
12010	→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Modus ponens 12008, 12009
12011	→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Modus ponens 12005, 12010
12012	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂, 𝜒↗𝜑] into ax-2
12013	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 12003, 12012
12014	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗¬¬𝜂] into ax-1
12015	→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 12013, 12014
12016	→→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
12017	→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 12015, 12016
12018	→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 12011, 12017
12019	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬¬𝜂] into ax-1
12020	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12021	→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 12019, 12020
12022	→→⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
12023	→→⋀⋀⋀𝜑𝜓𝜒𝜃⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 12021, 12022
12024	→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑	Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
12025	→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑	Modus ponens 12018, 12024
12026	→→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑	Subs [𝜑↗→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12027	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑	Modus ponens 12025, 12026
12028	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂𝜑] into ax-2
12029	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑	Modus ponens 12027, 12028
12030	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑	Modus ponens 12019, 12029
12031	→→𝜑¬¬𝜑→¬¬𝜂→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜂] into ax-1
12032	→¬¬𝜂→𝜑¬¬𝜑	Modus ponens notnot, 12031
12033	→→¬¬𝜂→𝜑¬¬𝜑→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑	Subs [𝜑↗¬¬𝜂, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
12034	→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑	Modus ponens 12032, 12033
12035	→→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑	Subs [𝜑↗→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12036	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑	Modus ponens 12034, 12035
12037	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂𝜑, 𝜒↗→¬¬𝜂¬¬𝜑] into ax-2
12038	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑	Modus ponens 12036, 12037
12039	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑	Modus ponens 12030, 12038
12040	→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂	Subs [𝜑↗¬𝜂, 𝜓↗¬𝜑] into ax-3
12041	→→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂	Subs [𝜑↗→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12042	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂	Modus ponens 12040, 12041
12043	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂¬¬𝜑, 𝜒↗→¬𝜑¬𝜂] into ax-2
12044	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂	Modus ponens 12042, 12043
12045	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂	Modus ponens 12039, 12044
12046	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜑¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜑, 𝜒↗¬𝜂] into ax-2
12047	→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12045, 12046
12048	→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12049	→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12047, 12048
12050	→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12051	→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜑→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12049, 12050
12052	→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 11741, 12051
12053	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into id
12054	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12055	→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12053, 12054
12056	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into notnotr
12057	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12058	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12059	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12057, 12058
12060	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12061	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12059, 12060
12062	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12056, 12061
12063	→→¬𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12064	→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12055, 12063
12065	→→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12066	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12064, 12065
12067	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12068	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12066, 12067
12069	→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12070	→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1
12071	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑	Modus ponens 12069, 12070
12072	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑] into ax-2
12073	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑	Modus ponens 12071, 12072
12074	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12075	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12062, 12074
12076	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12077	→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12075, 12076
12078	→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12079	→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12077, 12078
12080	→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12069, 12079
12081	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3
12082	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜑] into ax-1
12083	→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12081, 12082
12084	→→¬𝜑→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12085	→→¬𝜑→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12083, 12084
12086	→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12080, 12085
12087	→→¬𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12088	→→¬𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12086, 12087
12089	→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12052, 12088
12090	→→¬𝜑¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Subs [𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3
12091	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Modus ponens 12089, 12090
12092	→↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into biimp
12093	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12004, 12092
12094	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-1
12095	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Modus ponens 12091, 12094
12096	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜑] into ax-2
12097	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑	Modus ponens 12095, 12096
12098	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑	Modus ponens 12093, 12097
12099	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜏] into simpl
12100	→↔⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into bicom1
12101	↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Modus ponens 12004, 12100
12102	→↔¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into biimp
12103	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Modus ponens 12101, 12102
12104	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑	Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12105	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑	Modus ponens 12098, 12104
12106	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜑→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗𝜑] into ax-2
12107	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Modus ponens 12105, 12106
12108	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into pm3.2im
12109	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑, 𝜓↗𝜂] into ax-1
12110	→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑	Modus ponens 12091, 12109
12111	→→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜑→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑	Subs [𝜑↗𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜑] into ax-2
12112	→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑	Modus ponens 12110, 12111
12113	→→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑	Subs [𝜑↗→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12114	→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑	Modus ponens 12112, 12113
12115	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→𝜂𝜑] into ax-2
12116	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Modus ponens 12114, 12115
12117	→𝜂𝜂	Subs [𝜑↗𝜂] into id
12118	→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Subs [𝜑↗→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗𝜂] into ax-1
12119	→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Modus ponens 12006, 12118
12120	→→𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→→𝜂𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Subs [𝜑↗𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-2
12121	→→𝜂𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂	Modus ponens 12119, 12120
12122	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑, 𝜓↗𝜂] into ax-1
12123	→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 12013, 12122
12124	→→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑] into ax-2
12125	→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 12123, 12124
12126	→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑	Modus ponens 12006, 12125
12127	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂] into ax-1
12128	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12129	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 12127, 12128
12130	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-2
12131	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 12129, 12130
12132	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃	Modus ponens 12099, 12131
12133	→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜑] into ax-2
12134	→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Modus ponens 12126, 12133
12135	→→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Subs [𝜑↗→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12136	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑	Modus ponens 12134, 12135
12137	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜑] into ax-2
12138	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Modus ponens 12136, 12137
12139	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Modus ponens 12132, 12138
12140	→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12141	→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜂] into ax-1
12142	→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12140, 12141
12143	→→𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜂𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12144	→→𝜂𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12142, 12143
12145	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂, 𝜒↗𝜑] into ax-2
12146	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12139, 12145
12147	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗𝜂] into ax-1
12148	→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12146, 12147
12149	→→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12150	→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12148, 12149
12151	→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12140, 12150
12152	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into id
12153	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into ax-1
12154	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12155	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12153, 12154
12156	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12157	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12155, 12156
12158	→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12159	→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Modus ponens 12151, 12158
12160	→→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Subs [𝜑↗→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12161	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Modus ponens 12159, 12160
12162	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜑] into ax-2
12163	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Modus ponens 12161, 12162
12164	↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into df-an
12165	→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜂] into ax-1
12166	→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12140, 12165
12167	→→¬¬𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗¬¬𝜂, 𝜓↗𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12168	→→¬¬𝜂𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12166, 12167
12169	→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12005, 12168
12170	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗¬¬𝜂] into ax-1
12171	→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12146, 12170
12172	→→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12173	→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12171, 12172
12174	→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12169, 12173
12175	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜂] into ax-1
12176	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12177	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12175, 12176
12178	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12179	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12177, 12178
12180	→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑	Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12181	→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑	Modus ponens 12174, 12180
12182	→→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑	Subs [𝜑↗→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12183	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑	Modus ponens 12181, 12182
12184	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂𝜑] into ax-2
12185	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑	Modus ponens 12183, 12184
12186	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑	Modus ponens 12175, 12185
12187	→→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑	Subs [𝜑↗→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12188	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑	Modus ponens 12034, 12187
12189	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜑→¬¬𝜂¬¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂𝜑, 𝜒↗→¬¬𝜂¬¬𝜑] into ax-2
12190	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑	Modus ponens 12188, 12189
12191	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑	Modus ponens 12186, 12190
12192	→→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂	Subs [𝜑↗→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12193	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂	Modus ponens 12040, 12192
12194	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜑→¬𝜑¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂¬¬𝜑, 𝜒↗→¬𝜑¬𝜂] into ax-2
12195	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂	Modus ponens 12193, 12194
12196	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂	Modus ponens 12191, 12195
12197	→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12198	→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜓↗¬𝜑] into ax-1
12199	→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑	Modus ponens 12197, 12198
12200	→→¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑] into ax-2
12201	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑	Modus ponens 12199, 12200
12202	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜑, 𝜒↗¬𝜂] into ax-2
12203	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12196, 12202
12204	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12205	→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12203, 12204
12206	→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12207	→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12205, 12206
12208	→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12197, 12207
12209	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into id
12210	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12211	→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12209, 12210
12212	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into notnotr
12213	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12214	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12215	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12213, 12214
12216	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12217	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12215, 12216
12218	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12212, 12217
12219	→→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12220	→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12211, 12219
12221	→→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12222	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12220, 12221
12223	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12224	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12222, 12223
12225	→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12226	→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1
12227	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑	Modus ponens 12225, 12226
12228	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑] into ax-2
12229	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑	Modus ponens 12227, 12228
12230	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12231	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12218, 12230
12232	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12233	→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12231, 12232
12234	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12235	→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12233, 12234
12236	→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12225, 12235
12237	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3
12238	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜑] into ax-1
12239	→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12237, 12238
12240	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12241	→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12239, 12240
12242	→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12236, 12241
12243	→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12244	→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12242, 12243
12245	→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12208, 12244
12246	→→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3
12247	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑	Modus ponens 12245, 12246
12248	→↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into biimp
12249	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12164, 12248
12250	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12251	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑	Modus ponens 12247, 12250
12252	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗𝜑] into ax-2
12253	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12251, 12252
12254	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12249, 12253	simp-5l
12255	→→𝜓→𝜃𝜓→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓	Subs [𝜑↗→𝜓→𝜃𝜓, 𝜓↗⋀⋀𝜑𝜓𝜒] into ax-1
12256	→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓	Modus ponens 9774, 12255
12257	→→⋀⋀𝜑𝜓𝜒→𝜓→𝜃𝜓→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓	Subs [𝜑↗⋀⋀𝜑𝜓𝜒, 𝜒↗→𝜃𝜓] into ax-2
12258	→→⋀⋀𝜑𝜓𝜒𝜓→⋀⋀𝜑𝜓𝜒→𝜃𝜓	Modus ponens 12256, 12257
12259	→𝜓→𝜂𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜂] into ax-1
12260	→→𝜓→𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓	Subs [𝜑↗→𝜓→𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12261	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓	Modus ponens 12259, 12260
12262	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜓] into ax-2
12263	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Modus ponens 12261, 12262
12264	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Modus ponens simpllr, 12263
12265	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜂, 𝜒↗𝜓] into ax-2
12266	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 12264, 12265
12267	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗¬¬𝜂] into ax-1
12268	→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 12266, 12267
12269	→→¬¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
12270	→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 12268, 12269
12271	→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 12011, 12270
12272	→→¬¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓	Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
12273	→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓	Modus ponens 12271, 12272
12274	→→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓	Subs [𝜑↗→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12275	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓	Modus ponens 12273, 12274
12276	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→¬¬𝜂𝜓] into ax-2
12277	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓	Modus ponens 12275, 12276
12278	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓	Modus ponens 12019, 12277
12279	→→𝜓¬¬𝜓→¬¬𝜂→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜂] into ax-1
12280	→¬¬𝜂→𝜓¬¬𝜓	Modus ponens 448, 12279
12281	→→¬¬𝜂→𝜓¬¬𝜓→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓	Subs [𝜑↗¬¬𝜂, 𝜒↗¬¬𝜓] into ax-2
12282	→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓	Modus ponens 12280, 12281
12283	→→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓	Subs [𝜑↗→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12284	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓	Modus ponens 12282, 12283
12285	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂𝜓, 𝜒↗→¬¬𝜂¬¬𝜓] into ax-2
12286	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓	Modus ponens 12284, 12285
12287	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓	Modus ponens 12278, 12286
12288	→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂	Subs [𝜑↗¬𝜂, 𝜓↗¬𝜓] into ax-3
12289	→→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂	Subs [𝜑↗→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12290	→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂	Modus ponens 12288, 12289
12291	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→¬¬𝜂¬¬𝜓, 𝜒↗→¬𝜓¬𝜂] into ax-2
12292	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬¬𝜂¬¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂	Modus ponens 12290, 12291
12293	→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂	Modus ponens 12287, 12292
12294	→→⋀⋀⋀𝜑𝜓𝜒𝜃→¬𝜓¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗¬𝜓, 𝜒↗¬𝜂] into ax-2
12295	→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12293, 12294
12296	→→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12297	→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12295, 12296
12298	→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12299	→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜓→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12297, 12298
12300	→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 11941, 12299
12301	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12302	→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12053, 12301
12303	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12304	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12305	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12303, 12304
12306	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12307	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12305, 12306
12308	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12056, 12307
12309	→→¬𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12310	→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12302, 12309
12311	→→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12312	→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12310, 12311
12313	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12314	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12312, 12313
12315	→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12316	→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1
12317	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓	Modus ponens 12315, 12316
12318	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓] into ax-2
12319	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓	Modus ponens 12317, 12318
12320	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12321	→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12308, 12320
12322	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12323	→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12321, 12322
12324	→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12325	→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12323, 12324
12326	→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12315, 12325
12327	→→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗¬𝜓] into ax-1
12328	→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12081, 12327
12329	→→¬𝜓→→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12330	→→¬𝜓→¬¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12328, 12329
12331	→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12326, 12330
12332	→→¬𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-2
12333	→→¬𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12331, 12332
12334	→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂	Modus ponens 12300, 12333
12335	→→¬𝜓¬¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-3
12336	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Modus ponens 12334, 12335
12337	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂] into ax-1
12338	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Modus ponens 12336, 12337
12339	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜓] into ax-2
12340	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓	Modus ponens 12338, 12339
12341	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓	Modus ponens 12093, 12340
12342	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓	Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂] into ax-1
12343	→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓	Modus ponens 12341, 12342
12344	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂𝜓→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Subs [𝜑↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗𝜓] into ax-2
12345	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Modus ponens 12343, 12344
12346	→→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Subs [𝜑↗→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓, 𝜓↗𝜂] into ax-1
12347	→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓	Modus ponens 12336, 12346
12348	→→𝜂→¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂𝜓→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓	Subs [𝜑↗𝜂, 𝜓↗¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗𝜓] into ax-2
12349	→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓	Modus ponens 12347, 12348
12350	→→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓	Subs [𝜑↗→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12351	→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓	Modus ponens 12349, 12350
12352	→→⋀⋀⋀𝜑𝜓𝜒𝜃→→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→𝜂𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂, 𝜒↗→𝜂𝜓] into ax-2
12353	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂¬→⋀⋀⋀𝜑𝜓𝜒𝜃¬𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Modus ponens 12351, 12352
12354	→→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓, 𝜓↗𝜂] into ax-1
12355	→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 12266, 12354
12356	→→𝜂→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂, 𝜒↗→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓] into ax-2
12357	→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜂→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 12355, 12356
12358	→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓	Modus ponens 12006, 12357
12359	→→𝜂→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗𝜓] into ax-2
12360	→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Modus ponens 12358, 12359
12361	→→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Subs [𝜑↗→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12362	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓	Modus ponens 12360, 12361
12363	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜂𝜓] into ax-2
12364	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀𝜑𝜓𝜒𝜃→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Modus ponens 12362, 12363
12365	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Modus ponens 12132, 12364
12366	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂, 𝜒↗𝜓] into ax-2
12367	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12365, 12366
12368	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗𝜂] into ax-1
12369	→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12367, 12368
12370	→→𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12371	→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12369, 12370
12372	→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12140, 12371
12373	→→𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Subs [𝜑↗𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12374	→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Modus ponens 12372, 12373
12375	→→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Subs [𝜑↗→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12376	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Modus ponens 12374, 12375
12377	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜓] into ax-2
12378	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Modus ponens 12376, 12377
12379	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗¬¬𝜂] into ax-1
12380	→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12367, 12379
12381	→→¬¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗¬¬𝜂, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12382	→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12380, 12381
12383	→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12169, 12382
12384	→→¬¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓	Subs [𝜑↗¬¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12385	→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓	Modus ponens 12383, 12384
12386	→→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓	Subs [𝜑↗→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12387	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓	Modus ponens 12385, 12386
12388	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜂𝜓] into ax-2
12389	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓	Modus ponens 12387, 12388
12390	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓	Modus ponens 12175, 12389
12391	→→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓	Subs [𝜑↗→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12392	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓	Modus ponens 12282, 12391
12393	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂𝜓→¬¬𝜂¬¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂𝜓, 𝜒↗→¬¬𝜂¬¬𝜓] into ax-2
12394	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓	Modus ponens 12392, 12393
12395	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓	Modus ponens 12390, 12394
12396	→→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂	Subs [𝜑↗→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12397	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂	Modus ponens 12288, 12396
12398	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜂¬¬𝜓→¬𝜓¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜂¬¬𝜓, 𝜒↗→¬𝜓¬𝜂] into ax-2
12399	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜂¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂	Modus ponens 12397, 12398
12400	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂	Modus ponens 12395, 12399
12401	→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12402	→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜓↗¬𝜓] into ax-1
12403	→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓	Modus ponens 12401, 12402
12404	→→¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓] into ax-2
12405	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓	Modus ponens 12403, 12404
12406	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜓, 𝜒↗¬𝜂] into ax-2
12407	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12400, 12406
12408	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12409	→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12407, 12408
12410	→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12411	→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12409, 12410
12412	→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12401, 12411
12413	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12414	→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12209, 12413
12415	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12416	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12417	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12415, 12416
12418	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12419	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12417, 12418
12420	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12212, 12419
12421	→→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12422	→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12414, 12421
12423	→→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12424	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12422, 12423
12425	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12426	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12424, 12425
12427	→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-1
12428	→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1
12429	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓	Modus ponens 12427, 12428
12430	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓] into ax-2
12431	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓	Modus ponens 12429, 12430
12432	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12433	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12420, 12432
12434	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12435	→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12433, 12434
12436	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12437	→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12435, 12436
12438	→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12427, 12437
12439	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜓↗¬𝜓] into ax-1
12440	→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12237, 12439
12441	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12442	→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12440, 12441
12443	→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12438, 12442
12444	→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-2
12445	→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12443, 12444
12446	→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂	Modus ponens 12412, 12445
12447	→→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂] into ax-3
12448	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓	Modus ponens 12446, 12447
12449	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12450	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓	Modus ponens 12448, 12449
12451	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂, 𝜒↗𝜓] into ax-2
12452	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12450, 12451
12453	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12249, 12452	simp-5r
12454	→→𝜑→𝜏𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑	Subs [𝜑↗→𝜑→𝜏𝜑, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12455	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑	Modus ponens 11542, 12454
12456	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜑→𝜏𝜑→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜓↗𝜑, 𝜒↗→𝜏𝜑] into ax-2
12457	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜑→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜑	Modus ponens 12455, 12456
12458	→𝜑→𝜁𝜑	Subs [𝜓↗𝜁] into ax-1
12459	→→𝜑→𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑	Subs [𝜑↗→𝜑→𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12460	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑	Modus ponens 12458, 12459
12461	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜑, 𝜒↗→𝜁𝜑] into ax-2
12462	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Modus ponens 12460, 12461
12463	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Modus ponens simp-4l, 12462
12464	↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into df-an
12465	→¬¬𝜁𝜁	Subs [𝜑↗𝜁] into notnotr
12466	→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12467	→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Subs [𝜑↗→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬¬𝜁] into ax-1
12468	→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Modus ponens 12466, 12467
12469	→→¬¬𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Subs [𝜑↗¬¬𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-2
12470	→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Modus ponens 12468, 12469
12471	→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Modus ponens 12465, 12470
12472	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁, 𝜒↗𝜑] into ax-2
12473	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12463, 12472
12474	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗¬¬𝜁] into ax-1
12475	→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12473, 12474
12476	→→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12477	→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12475, 12476
12478	→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12471, 12477
12479	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬¬𝜁] into ax-1
12480	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12481	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12479, 12480
12482	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12483	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12481, 12482
12484	→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑	Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12485	→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑	Modus ponens 12478, 12484
12486	→→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑	Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12487	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑	Modus ponens 12485, 12486
12488	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁𝜑] into ax-2
12489	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑	Modus ponens 12487, 12488
12490	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑	Modus ponens 12479, 12489
12491	→→𝜑¬¬𝜑→¬¬𝜁→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜁] into ax-1
12492	→¬¬𝜁→𝜑¬¬𝜑	Modus ponens notnot, 12491
12493	→→¬¬𝜁→𝜑¬¬𝜑→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑	Subs [𝜑↗¬¬𝜁, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
12494	→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑	Modus ponens 12492, 12493
12495	→→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑	Subs [𝜑↗→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12496	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑	Modus ponens 12494, 12495
12497	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁𝜑, 𝜒↗→¬¬𝜁¬¬𝜑] into ax-2
12498	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑	Modus ponens 12496, 12497
12499	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑	Modus ponens 12490, 12498
12500	→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁	Subs [𝜑↗¬𝜁, 𝜓↗¬𝜑] into ax-3
12501	→→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁	Subs [𝜑↗→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12502	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁	Modus ponens 12500, 12501
12503	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁¬¬𝜑, 𝜒↗→¬𝜑¬𝜁] into ax-2
12504	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁	Modus ponens 12502, 12503
12505	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁	Modus ponens 12499, 12504
12506	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜑¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜑, 𝜒↗¬𝜁] into ax-2
12507	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12505, 12506
12508	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12509	→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12507, 12508
12510	→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12511	→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜑→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12509, 12510
12512	→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12197, 12511
12513	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into id
12514	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12515	→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12513, 12514
12516	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into notnotr
12517	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12518	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12519	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12517, 12518
12520	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12521	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12519, 12520
12522	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12516, 12521
12523	→→¬𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12524	→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12515, 12523
12525	→→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12526	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12524, 12525
12527	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12528	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12526, 12527
12529	→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12530	→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1
12531	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑	Modus ponens 12529, 12530
12532	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑] into ax-2
12533	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑	Modus ponens 12531, 12532
12534	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12535	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12522, 12534
12536	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12537	→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12535, 12536
12538	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12539	→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12537, 12538
12540	→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12529, 12539
12541	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3
12542	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜑] into ax-1
12543	→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12541, 12542
12544	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12545	→→¬𝜑→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12543, 12544
12546	→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12540, 12545
12547	→→¬𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12548	→→¬𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12546, 12547
12549	→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12512, 12548
12550	→→¬𝜑¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3
12551	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Modus ponens 12549, 12550
12552	→↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into biimp
12553	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12464, 12552
12554	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-1
12555	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Modus ponens 12551, 12554
12556	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜑] into ax-2
12557	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑	Modus ponens 12555, 12556
12558	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑	Modus ponens 12553, 12557
12559	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜂] into simpl
12560	→↔⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into bicom1
12561	↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Modus ponens 12464, 12560
12562	→↔¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into biimp
12563	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Modus ponens 12561, 12562
12564	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑	Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12565	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑	Modus ponens 12558, 12564
12566	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜑→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗𝜑] into ax-2
12567	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Modus ponens 12565, 12566
12568	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into pm3.2im
12569	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑, 𝜓↗𝜁] into ax-1
12570	→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑	Modus ponens 12551, 12569
12571	→→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜑→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑	Subs [𝜑↗𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜑] into ax-2
12572	→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑	Modus ponens 12570, 12571
12573	→→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑	Subs [𝜑↗→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12574	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑	Modus ponens 12572, 12573
12575	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→𝜁𝜑] into ax-2
12576	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Modus ponens 12574, 12575
12577	→𝜁𝜁	Subs [𝜑↗𝜁] into id
12578	→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Subs [𝜑↗→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗𝜁] into ax-1
12579	→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Modus ponens 12466, 12578
12580	→→𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→→𝜁𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Subs [𝜑↗𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-2
12581	→→𝜁𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁	Modus ponens 12579, 12580
12582	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑, 𝜓↗𝜁] into ax-1
12583	→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12473, 12582
12584	→→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑] into ax-2
12585	→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12583, 12584
12586	→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑	Modus ponens 12466, 12585
12587	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁] into ax-1
12588	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12589	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12587, 12588
12590	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-2
12591	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12589, 12590
12592	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏	Modus ponens 12559, 12591
12593	→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜑] into ax-2
12594	→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Modus ponens 12586, 12593
12595	→→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Subs [𝜑↗→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12596	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑	Modus ponens 12594, 12595
12597	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜑] into ax-2
12598	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Modus ponens 12596, 12597
12599	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Modus ponens 12592, 12598
12600	→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12601	→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜁] into ax-1
12602	→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 12600, 12601
12603	→→𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜁𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
12604	→→𝜁𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 12602, 12603
12605	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁, 𝜒↗𝜑] into ax-2
12606	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12599, 12605
12607	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗𝜁] into ax-1
12608	→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12606, 12607
12609	→→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
12610	→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12608, 12609
12611	→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12600, 12610
12612	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into id
12613	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into ax-1
12614	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12615	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12613, 12614
12616	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12617	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12615, 12616
12618	→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
12619	→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Modus ponens 12611, 12618
12620	→→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Subs [𝜑↗→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12621	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Modus ponens 12619, 12620
12622	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜑] into ax-2
12623	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Modus ponens 12621, 12622
12624	↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into df-an
12625	→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜁] into ax-1
12626	→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 12600, 12625
12627	→→¬¬𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗¬¬𝜁, 𝜓↗𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
12628	→→¬¬𝜁𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 12626, 12627
12629	→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 12465, 12628
12630	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗¬¬𝜁] into ax-1
12631	→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12606, 12630
12632	→→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
12633	→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12631, 12632
12634	→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12629, 12633
12635	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜁] into ax-1
12636	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12637	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12635, 12636
12638	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12639	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12637, 12638
12640	→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑	Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
12641	→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑	Modus ponens 12634, 12640
12642	→→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑	Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12643	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑	Modus ponens 12641, 12642
12644	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁𝜑] into ax-2
12645	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑	Modus ponens 12643, 12644
12646	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑	Modus ponens 12635, 12645
12647	→→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑	Subs [𝜑↗→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12648	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑	Modus ponens 12494, 12647
12649	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜑→¬¬𝜁¬¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁𝜑, 𝜒↗→¬¬𝜁¬¬𝜑] into ax-2
12650	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑	Modus ponens 12648, 12649
12651	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑	Modus ponens 12646, 12650
12652	→→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁	Subs [𝜑↗→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12653	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁	Modus ponens 12500, 12652
12654	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜑→¬𝜑¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁¬¬𝜑, 𝜒↗→¬𝜑¬𝜁] into ax-2
12655	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁	Modus ponens 12653, 12654
12656	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁	Modus ponens 12651, 12655
12657	→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12658	→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜓↗¬𝜑] into ax-1
12659	→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑	Modus ponens 12657, 12658
12660	→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑] into ax-2
12661	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑	Modus ponens 12659, 12660
12662	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜑, 𝜒↗¬𝜁] into ax-2
12663	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12656, 12662
12664	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12665	→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12663, 12664
12666	→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12667	→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12665, 12666
12668	→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12657, 12667
12669	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into id
12670	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12671	→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12669, 12670
12672	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into notnotr
12673	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12674	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12675	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12673, 12674
12676	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12677	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12675, 12676
12678	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12672, 12677
12679	→→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12680	→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12671, 12679
12681	→→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12682	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12680, 12681
12683	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12684	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12682, 12683
12685	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12686	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1
12687	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑	Modus ponens 12685, 12686
12688	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑] into ax-2
12689	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑	Modus ponens 12687, 12688
12690	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12691	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12678, 12690
12692	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12693	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12691, 12692
12694	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12695	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12693, 12694
12696	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12685, 12695
12697	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3
12698	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜑] into ax-1
12699	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12697, 12698
12700	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12701	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12699, 12700
12702	→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12696, 12701
12703	→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12704	→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12702, 12703
12705	→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12668, 12704
12706	→→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3
12707	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑	Modus ponens 12705, 12706
12708	→↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into biimp
12709	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12624, 12708
12710	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
12711	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑	Modus ponens 12707, 12710
12712	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗𝜑] into ax-2
12713	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 12711, 12712
12714	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 12709, 12713	simp-6l
12715	→→𝜓→𝜏𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓	Subs [𝜑↗→𝜓→𝜏𝜓, 𝜓↗⋀⋀⋀𝜑𝜓𝜒𝜃] into ax-1
12716	→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓	Modus ponens 11799, 12715
12717	→→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜓→𝜏𝜓→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Subs [𝜑↗⋀⋀⋀𝜑𝜓𝜒𝜃, 𝜒↗→𝜏𝜓] into ax-2
12718	→→⋀⋀⋀𝜑𝜓𝜒𝜃𝜓→⋀⋀⋀𝜑𝜓𝜒𝜃→𝜏𝜓	Modus ponens 12716, 12717
12719	→𝜓→𝜁𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜁] into ax-1
12720	→→𝜓→𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓	Subs [𝜑↗→𝜓→𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12721	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓	Modus ponens 12719, 12720
12722	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜓] into ax-2
12723	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Modus ponens 12721, 12722
12724	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Modus ponens simp-4r, 12723
12725	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜁, 𝜒↗𝜓] into ax-2
12726	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12724, 12725
12727	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗¬¬𝜁] into ax-1
12728	→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12726, 12727
12729	→→¬¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12730	→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12728, 12729
12731	→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12471, 12730
12732	→→¬¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓	Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12733	→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓	Modus ponens 12731, 12732
12734	→→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓	Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12735	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓	Modus ponens 12733, 12734
12736	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→¬¬𝜁𝜓] into ax-2
12737	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓	Modus ponens 12735, 12736
12738	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓	Modus ponens 12479, 12737
12739	→→𝜓¬¬𝜓→¬¬𝜁→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜁] into ax-1
12740	→¬¬𝜁→𝜓¬¬𝜓	Modus ponens 448, 12739
12741	→→¬¬𝜁→𝜓¬¬𝜓→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓	Subs [𝜑↗¬¬𝜁, 𝜒↗¬¬𝜓] into ax-2
12742	→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓	Modus ponens 12740, 12741
12743	→→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓	Subs [𝜑↗→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12744	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓	Modus ponens 12742, 12743
12745	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁𝜓, 𝜒↗→¬¬𝜁¬¬𝜓] into ax-2
12746	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓	Modus ponens 12744, 12745
12747	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓	Modus ponens 12738, 12746
12748	→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁	Subs [𝜑↗¬𝜁, 𝜓↗¬𝜓] into ax-3
12749	→→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁	Subs [𝜑↗→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12750	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁	Modus ponens 12748, 12749
12751	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→¬¬𝜁¬¬𝜓, 𝜒↗→¬𝜓¬𝜁] into ax-2
12752	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁	Modus ponens 12750, 12751
12753	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁	Modus ponens 12747, 12752
12754	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→¬𝜓¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗¬𝜓, 𝜒↗¬𝜁] into ax-2
12755	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12753, 12754
12756	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12757	→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12755, 12756
12758	→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12759	→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜓→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12757, 12758
12760	→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12401, 12759
12761	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12762	→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12513, 12761
12763	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12764	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12765	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12763, 12764
12766	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12767	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12765, 12766
12768	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12516, 12767
12769	→→¬𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12770	→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12762, 12769
12771	→→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12772	→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12770, 12771
12773	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12774	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12772, 12773
12775	→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12776	→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1
12777	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓	Modus ponens 12775, 12776
12778	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓] into ax-2
12779	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓	Modus ponens 12777, 12778
12780	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12781	→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12768, 12780
12782	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12783	→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12781, 12782
12784	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12785	→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12783, 12784
12786	→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12775, 12785
12787	→→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗¬𝜓] into ax-1
12788	→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12541, 12787
12789	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12790	→→¬𝜓→¬¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12788, 12789
12791	→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12786, 12790
12792	→→¬𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-2
12793	→→¬𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12791, 12792
12794	→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁	Modus ponens 12760, 12793
12795	→→¬𝜓¬¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-3
12796	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Modus ponens 12794, 12795
12797	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁] into ax-1
12798	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Modus ponens 12796, 12797
12799	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜓] into ax-2
12800	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓	Modus ponens 12798, 12799
12801	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓	Modus ponens 12553, 12800
12802	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓	Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁] into ax-1
12803	→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓	Modus ponens 12801, 12802
12804	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁𝜓→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Subs [𝜑↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗𝜓] into ax-2
12805	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Modus ponens 12803, 12804
12806	→→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓, 𝜓↗𝜁] into ax-1
12807	→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓	Modus ponens 12796, 12806
12808	→→𝜁→¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁𝜓→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓	Subs [𝜑↗𝜁, 𝜓↗¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗𝜓] into ax-2
12809	→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓	Modus ponens 12807, 12808
12810	→→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓	Subs [𝜑↗→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12811	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓	Modus ponens 12809, 12810
12812	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→𝜁𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁, 𝜒↗→𝜁𝜓] into ax-2
12813	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁¬→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏¬𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Modus ponens 12811, 12812
12814	→→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓, 𝜓↗𝜁] into ax-1
12815	→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12726, 12814
12816	→→𝜁→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁, 𝜒↗→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓] into ax-2
12817	→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜁→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12815, 12816
12818	→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓	Modus ponens 12466, 12817
12819	→→𝜁→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗𝜓] into ax-2
12820	→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Modus ponens 12818, 12819
12821	→→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Subs [𝜑↗→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12822	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓	Modus ponens 12820, 12821
12823	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜁𝜓] into ax-2
12824	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Modus ponens 12822, 12823
12825	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Modus ponens 12592, 12824
12826	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁, 𝜒↗𝜓] into ax-2
12827	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12825, 12826
12828	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗𝜁] into ax-1
12829	→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12827, 12828
12830	→→𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
12831	→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12829, 12830
12832	→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12600, 12831
12833	→→𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Subs [𝜑↗𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
12834	→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Modus ponens 12832, 12833
12835	→→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Subs [𝜑↗→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12836	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Modus ponens 12834, 12835
12837	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜓] into ax-2
12838	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Modus ponens 12836, 12837
12839	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗¬¬𝜁] into ax-1
12840	→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12827, 12839
12841	→→¬¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗¬¬𝜁, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
12842	→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12840, 12841
12843	→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12629, 12842
12844	→→¬¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓	Subs [𝜑↗¬¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
12845	→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓	Modus ponens 12843, 12844
12846	→→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓	Subs [𝜑↗→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12847	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓	Modus ponens 12845, 12846
12848	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜁𝜓] into ax-2
12849	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓	Modus ponens 12847, 12848
12850	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓	Modus ponens 12635, 12849
12851	→→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓	Subs [𝜑↗→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12852	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓	Modus ponens 12742, 12851
12853	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁𝜓→¬¬𝜁¬¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁𝜓, 𝜒↗→¬¬𝜁¬¬𝜓] into ax-2
12854	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓	Modus ponens 12852, 12853
12855	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓	Modus ponens 12850, 12854
12856	→→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁	Subs [𝜑↗→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12857	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁	Modus ponens 12748, 12856
12858	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜁¬¬𝜓→¬𝜓¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜁¬¬𝜓, 𝜒↗→¬𝜓¬𝜁] into ax-2
12859	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜁¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁	Modus ponens 12857, 12858
12860	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁	Modus ponens 12855, 12859
12861	→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12862	→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜓↗¬𝜓] into ax-1
12863	→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓	Modus ponens 12861, 12862
12864	→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓] into ax-2
12865	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓	Modus ponens 12863, 12864
12866	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜓, 𝜒↗¬𝜁] into ax-2
12867	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12860, 12866
12868	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12869	→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12867, 12868
12870	→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12871	→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12869, 12870
12872	→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12861, 12871
12873	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12874	→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12669, 12873
12875	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12876	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12877	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12875, 12876
12878	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12879	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12877, 12878
12880	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12672, 12879
12881	→→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12882	→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12874, 12881
12883	→→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12884	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12882, 12883
12885	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12886	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12884, 12885
12887	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-1
12888	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1
12889	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓	Modus ponens 12887, 12888
12890	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓] into ax-2
12891	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓	Modus ponens 12889, 12890
12892	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12893	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12880, 12892
12894	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12895	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12893, 12894
12896	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12897	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12895, 12896
12898	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12887, 12897
12899	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜓↗¬𝜓] into ax-1
12900	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12697, 12899
12901	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12902	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12900, 12901
12903	→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12898, 12902
12904	→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-2
12905	→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12903, 12904
12906	→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁	Modus ponens 12872, 12905
12907	→→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁] into ax-3
12908	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓	Modus ponens 12906, 12907
12909	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
12910	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓	Modus ponens 12908, 12909
12911	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁, 𝜒↗𝜓] into ax-2
12912	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 12910, 12911
12913	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 12709, 12912	simp-6r
12914	→→𝜑→𝜂𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑	Subs [𝜑↗→𝜑→𝜂𝜑, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
12915	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑	Modus ponens 11998, 12914
12916	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜑→𝜂𝜑→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜓↗𝜑, 𝜒↗→𝜂𝜑] into ax-2
12917	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜑→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜑	Modus ponens 12915, 12916
12918	→𝜑→𝜎𝜑	Subs [𝜓↗𝜎] into ax-1
12919	→→𝜑→𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑	Subs [𝜑↗→𝜑→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12920	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑	Modus ponens 12918, 12919
12921	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜑, 𝜒↗→𝜎𝜑] into ax-2
12922	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Modus ponens 12920, 12921
12923	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Modus ponens simp-5l, 12922
12924	↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into df-an
12925	→¬¬𝜎𝜎	Subs [𝜑↗𝜎] into notnotr
12926	→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12927	→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬¬𝜎] into ax-1
12928	→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Modus ponens 12926, 12927
12929	→→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Subs [𝜑↗¬¬𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-2
12930	→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Modus ponens 12928, 12929
12931	→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Modus ponens 12925, 12930
12932	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎, 𝜒↗𝜑] into ax-2
12933	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12923, 12932
12934	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗¬¬𝜎] into ax-1
12935	→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12933, 12934
12936	→→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
12937	→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12935, 12936
12938	→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12931, 12937
12939	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬¬𝜎] into ax-1
12940	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12941	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12939, 12940
12942	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
12943	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 12941, 12942
12944	→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑	Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
12945	→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑	Modus ponens 12938, 12944
12946	→→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑	Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12947	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑	Modus ponens 12945, 12946
12948	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎𝜑] into ax-2
12949	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑	Modus ponens 12947, 12948
12950	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑	Modus ponens 12939, 12949
12951	→→𝜑¬¬𝜑→¬¬𝜎→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜎] into ax-1
12952	→¬¬𝜎→𝜑¬¬𝜑	Modus ponens notnot, 12951
12953	→→¬¬𝜎→𝜑¬¬𝜑→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑	Subs [𝜑↗¬¬𝜎, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
12954	→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑	Modus ponens 12952, 12953
12955	→→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑	Subs [𝜑↗→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12956	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑	Modus ponens 12954, 12955
12957	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎𝜑, 𝜒↗→¬¬𝜎¬¬𝜑] into ax-2
12958	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑	Modus ponens 12956, 12957
12959	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑	Modus ponens 12950, 12958
12960	→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎	Subs [𝜑↗¬𝜎, 𝜓↗¬𝜑] into ax-3
12961	→→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎	Subs [𝜑↗→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
12962	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎	Modus ponens 12960, 12961
12963	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎¬¬𝜑, 𝜒↗→¬𝜑¬𝜎] into ax-2
12964	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎	Modus ponens 12962, 12963
12965	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎	Modus ponens 12959, 12964
12966	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜑, 𝜒↗¬𝜎] into ax-2
12967	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12965, 12966
12968	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12969	→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12967, 12968
12970	→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12971	→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜑→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12969, 12970
12972	→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12657, 12971
12973	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into id
12974	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12975	→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12973, 12974
12976	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into notnotr
12977	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12978	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
12979	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12977, 12978
12980	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12981	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12979, 12980
12982	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12976, 12981
12983	→→¬𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12984	→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12975, 12983
12985	→→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
12986	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12984, 12985
12987	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12988	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12986, 12987
12989	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
12990	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1
12991	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑	Modus ponens 12989, 12990
12992	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑] into ax-2
12993	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑	Modus ponens 12991, 12992
12994	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12995	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12982, 12994
12996	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
12997	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12995, 12996
12998	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
12999	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12997, 12998
13000	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12989, 12999
13001	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3
13002	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜑] into ax-1
13003	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13001, 13002
13004	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13005	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13003, 13004
13006	→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13000, 13005
13007	→→¬𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13008	→→¬𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13006, 13007
13009	→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12972, 13008
13010	→→¬𝜑¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3
13011	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Modus ponens 13009, 13010
13012	→↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into biimp
13013	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12924, 13012
13014	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-1
13015	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Modus ponens 13011, 13014
13016	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜑] into ax-2
13017	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑	Modus ponens 13015, 13016
13018	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑	Modus ponens 13013, 13017
13019	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜁] into simpl
13020	→↔⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into bicom1
13021	↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Modus ponens 12924, 13020
13022	→↔¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into biimp
13023	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Modus ponens 13021, 13022
13024	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13025	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑	Modus ponens 13018, 13024
13026	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜑→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗𝜑] into ax-2
13027	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Modus ponens 13025, 13026
13028	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into pm3.2im
13029	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑, 𝜓↗𝜎] into ax-1
13030	→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑	Modus ponens 13011, 13029
13031	→→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜑→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑	Subs [𝜑↗𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜑] into ax-2
13032	→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑	Modus ponens 13030, 13031
13033	→→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑	Subs [𝜑↗→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13034	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑	Modus ponens 13032, 13033
13035	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→𝜎𝜑] into ax-2
13036	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Modus ponens 13034, 13035
13037	→𝜎𝜎	Subs [𝜑↗𝜎] into id
13038	→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗𝜎] into ax-1
13039	→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Modus ponens 12926, 13038
13040	→→𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Subs [𝜑↗𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-2
13041	→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎	Modus ponens 13039, 13040
13042	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑, 𝜓↗𝜎] into ax-1
13043	→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12933, 13042
13044	→→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑] into ax-2
13045	→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 13043, 13044
13046	→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑	Modus ponens 12926, 13045
13047	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎] into ax-1
13048	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13049	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 13047, 13048
13050	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-2
13051	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 13049, 13050
13052	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂	Modus ponens 13019, 13051
13053	→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜑] into ax-2
13054	→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Modus ponens 13046, 13053
13055	→→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13056	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑	Modus ponens 13054, 13055
13057	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜑] into ax-2
13058	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Modus ponens 13056, 13057
13059	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Modus ponens 13052, 13058
13060	→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13061	→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜎] into ax-1
13062	→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13060, 13061
13063	→→𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13064	→→𝜎𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13062, 13063
13065	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎, 𝜒↗𝜑] into ax-2
13066	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13059, 13065
13067	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗𝜎] into ax-1
13068	→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13066, 13067
13069	→→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13070	→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13068, 13069
13071	→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13060, 13070
13072	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into id
13073	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into ax-1
13074	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13075	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13073, 13074
13076	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13077	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13075, 13076
13078	→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13079	→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Modus ponens 13071, 13078
13080	→→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13081	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Modus ponens 13079, 13080
13082	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜑] into ax-2
13083	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Modus ponens 13081, 13082
13084	↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into df-an
13085	→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜎] into ax-1
13086	→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13060, 13085
13087	→→¬¬𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗¬¬𝜎, 𝜓↗𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13088	→→¬¬𝜎𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13086, 13087
13089	→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 12925, 13088
13090	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗¬¬𝜎] into ax-1
13091	→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13066, 13090
13092	→→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13093	→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13091, 13092
13094	→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13089, 13093
13095	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜎] into ax-1
13096	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13097	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13095, 13096
13098	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13099	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13097, 13098
13100	→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑	Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13101	→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑	Modus ponens 13094, 13100
13102	→→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑	Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13103	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑	Modus ponens 13101, 13102
13104	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎𝜑] into ax-2
13105	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑	Modus ponens 13103, 13104
13106	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑	Modus ponens 13095, 13105
13107	→→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑	Subs [𝜑↗→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13108	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑	Modus ponens 12954, 13107
13109	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜑→¬¬𝜎¬¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎𝜑, 𝜒↗→¬¬𝜎¬¬𝜑] into ax-2
13110	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑	Modus ponens 13108, 13109
13111	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑	Modus ponens 13106, 13110
13112	→→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎	Subs [𝜑↗→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13113	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎	Modus ponens 12960, 13112
13114	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜑→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎¬¬𝜑, 𝜒↗→¬𝜑¬𝜎] into ax-2
13115	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎	Modus ponens 13113, 13114
13116	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎	Modus ponens 13111, 13115
13117	→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13118	→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜓↗¬𝜑] into ax-1
13119	→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑	Modus ponens 13117, 13118
13120	→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑] into ax-2
13121	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑	Modus ponens 13119, 13120
13122	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜑, 𝜒↗¬𝜎] into ax-2
13123	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13116, 13122
13124	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13125	→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13123, 13124
13126	→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13127	→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13125, 13126
13128	→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13117, 13127
13129	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into id
13130	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13131	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13129, 13130
13132	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into notnotr
13133	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13134	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13135	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13133, 13134
13136	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13137	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13135, 13136
13138	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13132, 13137
13139	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13140	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13131, 13139
13141	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13142	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13140, 13141
13143	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13144	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13142, 13143
13145	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13146	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1
13147	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑	Modus ponens 13145, 13146
13148	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑] into ax-2
13149	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑	Modus ponens 13147, 13148
13150	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13151	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13138, 13150
13152	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13153	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13151, 13152
13154	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13155	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13153, 13154
13156	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13145, 13155
13157	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3
13158	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜑] into ax-1
13159	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13157, 13158
13160	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13161	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13159, 13160
13162	→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13156, 13161
13163	→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13164	→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13162, 13163
13165	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13128, 13164
13166	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3
13167	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑	Modus ponens 13165, 13166
13168	→↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into biimp
13169	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13084, 13168
13170	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13171	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑	Modus ponens 13167, 13170
13172	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗𝜑] into ax-2
13173	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13171, 13172
13174	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13169, 13173	simp-7l
13175	→→𝜓→𝜂𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓	Subs [𝜑↗→𝜓→𝜂𝜓, 𝜓↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏] into ax-1
13176	→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓	Modus ponens 12259, 13175
13177	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜓→𝜂𝜓→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏, 𝜒↗→𝜂𝜓] into ax-2
13178	→→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜓→⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏→𝜂𝜓	Modus ponens 13176, 13177
13179	→𝜓→𝜎𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜎] into ax-1
13180	→→𝜓→𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓	Subs [𝜑↗→𝜓→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13181	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓	Modus ponens 13179, 13180
13182	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜓] into ax-2
13183	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Modus ponens 13181, 13182
13184	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Modus ponens simp-5r, 13183
13185	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜎, 𝜒↗𝜓] into ax-2
13186	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 13184, 13185
13187	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗¬¬𝜎] into ax-1
13188	→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 13186, 13187
13189	→→¬¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
13190	→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 13188, 13189
13191	→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12931, 13190
13192	→→¬¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓	Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
13193	→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓	Modus ponens 13191, 13192
13194	→→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓	Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13195	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓	Modus ponens 13193, 13194
13196	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→¬¬𝜎𝜓] into ax-2
13197	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓	Modus ponens 13195, 13196
13198	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓	Modus ponens 12939, 13197
13199	→→𝜓¬¬𝜓→¬¬𝜎→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜎] into ax-1
13200	→¬¬𝜎→𝜓¬¬𝜓	Modus ponens 448, 13199
13201	→→¬¬𝜎→𝜓¬¬𝜓→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓	Subs [𝜑↗¬¬𝜎, 𝜒↗¬¬𝜓] into ax-2
13202	→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓	Modus ponens 13200, 13201
13203	→→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓	Subs [𝜑↗→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13204	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓	Modus ponens 13202, 13203
13205	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎𝜓, 𝜒↗→¬¬𝜎¬¬𝜓] into ax-2
13206	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓	Modus ponens 13204, 13205
13207	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓	Modus ponens 13198, 13206
13208	→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎	Subs [𝜑↗¬𝜎, 𝜓↗¬𝜓] into ax-3
13209	→→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎	Subs [𝜑↗→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13210	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎	Modus ponens 13208, 13209
13211	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→¬¬𝜎¬¬𝜓, 𝜒↗→¬𝜓¬𝜎] into ax-2
13212	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎	Modus ponens 13210, 13211
13213	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎	Modus ponens 13207, 13212
13214	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗¬𝜓, 𝜒↗¬𝜎] into ax-2
13215	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13213, 13214
13216	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13217	→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13215, 13216
13218	→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13219	→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜓→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13217, 13218
13220	→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12861, 13219
13221	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13222	→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12973, 13221
13223	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13224	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13225	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13223, 13224
13226	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13227	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13225, 13226
13228	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 12976, 13227
13229	→→¬𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13230	→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13222, 13229
13231	→→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13232	→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13230, 13231
13233	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13234	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13232, 13233
13235	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13236	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1
13237	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓	Modus ponens 13235, 13236
13238	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓] into ax-2
13239	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓	Modus ponens 13237, 13238
13240	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13241	→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13228, 13240
13242	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13243	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13241, 13242
13244	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13245	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13243, 13244
13246	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13235, 13245
13247	→→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗¬𝜓] into ax-1
13248	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13001, 13247
13249	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13250	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13248, 13249
13251	→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13246, 13250
13252	→→¬𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-2
13253	→→¬𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13251, 13252
13254	→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎	Modus ponens 13220, 13253
13255	→→¬𝜓¬¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-3
13256	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Modus ponens 13254, 13255
13257	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎] into ax-1
13258	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Modus ponens 13256, 13257
13259	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜓] into ax-2
13260	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓	Modus ponens 13258, 13259
13261	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓	Modus ponens 13013, 13260
13262	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎] into ax-1
13263	→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓	Modus ponens 13261, 13262
13264	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎𝜓→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Subs [𝜑↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗𝜓] into ax-2
13265	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Modus ponens 13263, 13264
13266	→→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓, 𝜓↗𝜎] into ax-1
13267	→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓	Modus ponens 13256, 13266
13268	→→𝜎→¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎𝜓→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓	Subs [𝜑↗𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗𝜓] into ax-2
13269	→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓	Modus ponens 13267, 13268
13270	→→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓	Subs [𝜑↗→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13271	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓	Modus ponens 13269, 13270
13272	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→𝜎𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎, 𝜒↗→𝜎𝜓] into ax-2
13273	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎¬→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂¬𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Modus ponens 13271, 13272
13274	→→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓, 𝜓↗𝜎] into ax-1
13275	→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 13186, 13274
13276	→→𝜎→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎, 𝜒↗→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓] into ax-2
13277	→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜎→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 13275, 13276
13278	→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓	Modus ponens 12926, 13277
13279	→→𝜎→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗𝜓] into ax-2
13280	→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Modus ponens 13278, 13279
13281	→→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13282	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓	Modus ponens 13280, 13281
13283	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜎𝜓] into ax-2
13284	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Modus ponens 13282, 13283
13285	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Modus ponens 13052, 13284
13286	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎, 𝜒↗𝜓] into ax-2
13287	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13285, 13286
13288	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗𝜎] into ax-1
13289	→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13287, 13288
13290	→→𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13291	→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13289, 13290
13292	→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13060, 13291
13293	→→𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Subs [𝜑↗𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13294	→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Modus ponens 13292, 13293
13295	→→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Subs [𝜑↗→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13296	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Modus ponens 13294, 13295
13297	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜓] into ax-2
13298	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Modus ponens 13296, 13297
13299	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗¬¬𝜎] into ax-1
13300	→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13287, 13299
13301	→→¬¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗¬¬𝜎, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13302	→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13300, 13301
13303	→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13089, 13302
13304	→→¬¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓	Subs [𝜑↗¬¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13305	→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓	Modus ponens 13303, 13304
13306	→→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓	Subs [𝜑↗→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13307	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓	Modus ponens 13305, 13306
13308	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜎𝜓] into ax-2
13309	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓	Modus ponens 13307, 13308
13310	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓	Modus ponens 13095, 13309
13311	→→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓	Subs [𝜑↗→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13312	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓	Modus ponens 13202, 13311
13313	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎𝜓→¬¬𝜎¬¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎𝜓, 𝜒↗→¬¬𝜎¬¬𝜓] into ax-2
13314	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓	Modus ponens 13312, 13313
13315	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓	Modus ponens 13310, 13314
13316	→→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎	Subs [𝜑↗→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13317	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎	Modus ponens 13208, 13316
13318	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜎¬¬𝜓→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜎¬¬𝜓, 𝜒↗→¬𝜓¬𝜎] into ax-2
13319	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜎¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎	Modus ponens 13317, 13318
13320	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎	Modus ponens 13315, 13319
13321	→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13322	→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜓↗¬𝜓] into ax-1
13323	→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓	Modus ponens 13321, 13322
13324	→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓] into ax-2
13325	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓	Modus ponens 13323, 13324
13326	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜓, 𝜒↗¬𝜎] into ax-2
13327	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13320, 13326
13328	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13329	→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13327, 13328
13330	→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13331	→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13329, 13330
13332	→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13321, 13331
13333	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13334	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13129, 13333
13335	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13336	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13337	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13335, 13336
13338	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13339	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13337, 13338
13340	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13132, 13339
13341	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13342	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13334, 13341
13343	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13344	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13342, 13343
13345	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13346	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13344, 13345
13347	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-1
13348	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1
13349	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓	Modus ponens 13347, 13348
13350	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓] into ax-2
13351	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓	Modus ponens 13349, 13350
13352	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13353	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13340, 13352
13354	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13355	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13353, 13354
13356	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13357	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13355, 13356
13358	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13347, 13357
13359	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜓↗¬𝜓] into ax-1
13360	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13157, 13359
13361	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13362	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13360, 13361
13363	→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13358, 13362
13364	→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-2
13365	→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13363, 13364
13366	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎	Modus ponens 13332, 13365
13367	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎] into ax-3
13368	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓	Modus ponens 13366, 13367
13369	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13370	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓	Modus ponens 13368, 13369
13371	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎, 𝜒↗𝜓] into ax-2
13372	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13370, 13371
13373	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13169, 13372	simp-7r
13374	→→𝜑→𝜁𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑	Subs [𝜑↗→𝜑→𝜁𝜑, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13375	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑	Modus ponens 12458, 13374
13376	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜑→𝜁𝜑→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜓↗𝜑, 𝜒↗→𝜁𝜑] into ax-2
13377	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜑→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜑	Modus ponens 13375, 13376
13378	→𝜑→𝜌𝜑	Subs [𝜓↗𝜌] into ax-1
13379	→→𝜑→𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑	Subs [𝜑↗→𝜑→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13380	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑	Modus ponens 13378, 13379
13381	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜑, 𝜒↗→𝜌𝜑] into ax-2
13382	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Modus ponens 13380, 13381
13383	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Modus ponens simp-6l, 13382
13384	↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into df-an
13385	→¬¬𝜌𝜌	Subs [𝜑↗𝜌] into notnotr
13386	→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13387	→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬¬𝜌] into ax-1
13388	→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Modus ponens 13386, 13387
13389	→→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Subs [𝜑↗¬¬𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-2
13390	→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Modus ponens 13388, 13389
13391	→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Modus ponens 13385, 13390
13392	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌, 𝜒↗𝜑] into ax-2
13393	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13383, 13392
13394	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗¬¬𝜌] into ax-1
13395	→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13393, 13394
13396	→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13397	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13395, 13396
13398	→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13391, 13397
13399	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬¬𝜌] into ax-1
13400	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13401	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13399, 13400
13402	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13403	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13401, 13402
13404	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑	Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13405	→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑	Modus ponens 13398, 13404
13406	→→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑	Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13407	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑	Modus ponens 13405, 13406
13408	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌𝜑] into ax-2
13409	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑	Modus ponens 13407, 13408
13410	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑	Modus ponens 13399, 13409
13411	→→𝜑¬¬𝜑→¬¬𝜌→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜌] into ax-1
13412	→¬¬𝜌→𝜑¬¬𝜑	Modus ponens notnot, 13411
13413	→→¬¬𝜌→𝜑¬¬𝜑→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑	Subs [𝜑↗¬¬𝜌, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
13414	→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑	Modus ponens 13412, 13413
13415	→→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑	Subs [𝜑↗→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13416	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑	Modus ponens 13414, 13415
13417	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌𝜑, 𝜒↗→¬¬𝜌¬¬𝜑] into ax-2
13418	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑	Modus ponens 13416, 13417
13419	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑	Modus ponens 13410, 13418
13420	→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌	Subs [𝜑↗¬𝜌, 𝜓↗¬𝜑] into ax-3
13421	→→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌	Subs [𝜑↗→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13422	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌	Modus ponens 13420, 13421
13423	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌¬¬𝜑, 𝜒↗→¬𝜑¬𝜌] into ax-2
13424	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌	Modus ponens 13422, 13423
13425	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌	Modus ponens 13419, 13424
13426	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜑, 𝜒↗¬𝜌] into ax-2
13427	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13425, 13426
13428	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13429	→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13427, 13428
13430	→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13431	→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13429, 13430
13432	→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13117, 13431
13433	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into id
13434	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13435	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13433, 13434
13436	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into notnotr
13437	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13438	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13439	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13437, 13438
13440	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13441	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13439, 13440
13442	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13436, 13441
13443	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13444	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13435, 13443
13445	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13446	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13444, 13445
13447	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13448	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13446, 13447
13449	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13450	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1
13451	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑	Modus ponens 13449, 13450
13452	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑] into ax-2
13453	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑	Modus ponens 13451, 13452
13454	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13455	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13442, 13454
13456	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13457	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13455, 13456
13458	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13459	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13457, 13458
13460	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13449, 13459
13461	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3
13462	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜑] into ax-1
13463	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13461, 13462
13464	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13465	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13463, 13464
13466	→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13460, 13465
13467	→→¬𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13468	→→¬𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13466, 13467
13469	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13432, 13468
13470	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3
13471	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Modus ponens 13469, 13470
13472	→↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into biimp
13473	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13384, 13472
13474	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-1
13475	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Modus ponens 13471, 13474
13476	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜑] into ax-2
13477	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑	Modus ponens 13475, 13476
13478	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑	Modus ponens 13473, 13477
13479	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜎] into simpl
13480	→↔⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into bicom1
13481	↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Modus ponens 13384, 13480
13482	→↔¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into biimp
13483	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Modus ponens 13481, 13482
13484	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13485	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑	Modus ponens 13478, 13484
13486	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜑→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗𝜑] into ax-2
13487	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Modus ponens 13485, 13486
13488	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into pm3.2im
13489	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑, 𝜓↗𝜌] into ax-1
13490	→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑	Modus ponens 13471, 13489
13491	→→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜑→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑	Subs [𝜑↗𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜑] into ax-2
13492	→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑	Modus ponens 13490, 13491
13493	→→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑	Subs [𝜑↗→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13494	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑	Modus ponens 13492, 13493
13495	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→𝜌𝜑] into ax-2
13496	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Modus ponens 13494, 13495
13497	→𝜌𝜌	Subs [𝜑↗𝜌] into id
13498	→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗𝜌] into ax-1
13499	→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Modus ponens 13386, 13498
13500	→→𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Subs [𝜑↗𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-2
13501	→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌	Modus ponens 13499, 13500
13502	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑, 𝜓↗𝜌] into ax-1
13503	→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13393, 13502
13504	→→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑] into ax-2
13505	→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13503, 13504
13506	→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑	Modus ponens 13386, 13505
13507	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌] into ax-1
13508	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13509	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13507, 13508
13510	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-2
13511	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13509, 13510
13512	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁	Modus ponens 13479, 13511
13513	→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜑] into ax-2
13514	→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Modus ponens 13506, 13513
13515	→→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13516	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑	Modus ponens 13514, 13515
13517	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜑] into ax-2
13518	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Modus ponens 13516, 13517
13519	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Modus ponens 13512, 13518
13520	→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13521	→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜌] into ax-1
13522	→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 13520, 13521
13523	→→𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
13524	→→𝜌𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 13522, 13523
13525	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌, 𝜒↗𝜑] into ax-2
13526	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13519, 13525
13527	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗𝜌] into ax-1
13528	→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13526, 13527
13529	→→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13530	→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13528, 13529
13531	→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13520, 13530
13532	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into id
13533	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into ax-1
13534	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13535	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13533, 13534
13536	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13537	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13535, 13536
13538	→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13539	→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Modus ponens 13531, 13538
13540	→→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13541	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Modus ponens 13539, 13540
13542	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜑] into ax-2
13543	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Modus ponens 13541, 13542
13544	↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into df-an
13545	→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜌] into ax-1
13546	→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 13520, 13545
13547	→→¬¬𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗¬¬𝜌, 𝜓↗𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
13548	→→¬¬𝜌𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 13546, 13547
13549	→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 13385, 13548
13550	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗¬¬𝜌] into ax-1
13551	→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13526, 13550
13552	→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13553	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13551, 13552
13554	→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13549, 13553
13555	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜌] into ax-1
13556	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13557	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13555, 13556
13558	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13559	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13557, 13558
13560	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑	Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13561	→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑	Modus ponens 13554, 13560
13562	→→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑	Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13563	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑	Modus ponens 13561, 13562
13564	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌𝜑] into ax-2
13565	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑	Modus ponens 13563, 13564
13566	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑	Modus ponens 13555, 13565
13567	→→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑	Subs [𝜑↗→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13568	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑	Modus ponens 13414, 13567
13569	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜑→¬¬𝜌¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌𝜑, 𝜒↗→¬¬𝜌¬¬𝜑] into ax-2
13570	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑	Modus ponens 13568, 13569
13571	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑	Modus ponens 13566, 13570
13572	→→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌	Subs [𝜑↗→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13573	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌	Modus ponens 13420, 13572
13574	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜑→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌¬¬𝜑, 𝜒↗→¬𝜑¬𝜌] into ax-2
13575	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌	Modus ponens 13573, 13574
13576	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌	Modus ponens 13571, 13575
13577	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13578	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜓↗¬𝜑] into ax-1
13579	→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑	Modus ponens 13577, 13578
13580	→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑] into ax-2
13581	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑	Modus ponens 13579, 13580
13582	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜑, 𝜒↗¬𝜌] into ax-2
13583	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13576, 13582
13584	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13585	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13583, 13584
13586	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13587	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13585, 13586
13588	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13577, 13587
13589	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into id
13590	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13591	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13589, 13590
13592	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into notnotr
13593	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13594	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13595	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13593, 13594
13596	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13597	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13595, 13596
13598	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13592, 13597
13599	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13600	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13591, 13599
13601	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13602	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13600, 13601
13603	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13604	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13602, 13603
13605	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13606	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1
13607	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑	Modus ponens 13605, 13606
13608	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑] into ax-2
13609	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑	Modus ponens 13607, 13608
13610	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13611	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13598, 13610
13612	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13613	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13611, 13612
13614	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13615	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13613, 13614
13616	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13605, 13615
13617	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3
13618	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜑] into ax-1
13619	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13617, 13618
13620	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13621	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13619, 13620
13622	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13616, 13621
13623	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13624	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13622, 13623
13625	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13588, 13624
13626	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3
13627	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑	Modus ponens 13625, 13626
13628	→↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into biimp
13629	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13544, 13628
13630	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13631	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑	Modus ponens 13627, 13630
13632	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗𝜑] into ax-2
13633	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 13631, 13632
13634	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 13629, 13633	simp-8l
13635	→→𝜓→𝜁𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓	Subs [𝜑↗→𝜓→𝜁𝜓, 𝜓↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂] into ax-1
13636	→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓	Modus ponens 12719, 13635
13637	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜓→𝜁𝜓→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂, 𝜒↗→𝜁𝜓] into ax-2
13638	→→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜓→⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂→𝜁𝜓	Modus ponens 13636, 13637
13639	→𝜓→𝜌𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜌] into ax-1
13640	→→𝜓→𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓	Subs [𝜑↗→𝜓→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13641	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓	Modus ponens 13639, 13640
13642	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜓] into ax-2
13643	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Modus ponens 13641, 13642
13644	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Modus ponens simp-6r, 13643
13645	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜌, 𝜒↗𝜓] into ax-2
13646	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13644, 13645
13647	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗¬¬𝜌] into ax-1
13648	→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13646, 13647
13649	→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13650	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13648, 13649
13651	→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13391, 13650
13652	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓	Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13653	→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓	Modus ponens 13651, 13652
13654	→→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓	Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13655	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓	Modus ponens 13653, 13654
13656	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→¬¬𝜌𝜓] into ax-2
13657	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓	Modus ponens 13655, 13656
13658	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓	Modus ponens 13399, 13657
13659	→→𝜓¬¬𝜓→¬¬𝜌→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜌] into ax-1
13660	→¬¬𝜌→𝜓¬¬𝜓	Modus ponens 448, 13659
13661	→→¬¬𝜌→𝜓¬¬𝜓→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓	Subs [𝜑↗¬¬𝜌, 𝜒↗¬¬𝜓] into ax-2
13662	→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓	Modus ponens 13660, 13661
13663	→→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓	Subs [𝜑↗→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13664	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓	Modus ponens 13662, 13663
13665	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌𝜓, 𝜒↗→¬¬𝜌¬¬𝜓] into ax-2
13666	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓	Modus ponens 13664, 13665
13667	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓	Modus ponens 13658, 13666
13668	→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌	Subs [𝜑↗¬𝜌, 𝜓↗¬𝜓] into ax-3
13669	→→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌	Subs [𝜑↗→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13670	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌	Modus ponens 13668, 13669
13671	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→¬¬𝜌¬¬𝜓, 𝜒↗→¬𝜓¬𝜌] into ax-2
13672	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌	Modus ponens 13670, 13671
13673	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌	Modus ponens 13667, 13672
13674	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗¬𝜓, 𝜒↗¬𝜌] into ax-2
13675	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13673, 13674
13676	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13677	→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13675, 13676
13678	→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13679	→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13677, 13678
13680	→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13321, 13679
13681	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13682	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13433, 13681
13683	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13684	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13685	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13683, 13684
13686	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13687	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13685, 13686
13688	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13436, 13687
13689	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13690	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13682, 13689
13691	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13692	→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13690, 13691
13693	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13694	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13692, 13693
13695	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13696	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1
13697	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓	Modus ponens 13695, 13696
13698	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓] into ax-2
13699	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓	Modus ponens 13697, 13698
13700	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13701	→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13688, 13700
13702	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13703	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13701, 13702
13704	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13705	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13703, 13704
13706	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13695, 13705
13707	→→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗¬𝜓] into ax-1
13708	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13461, 13707
13709	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13710	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13708, 13709
13711	→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13706, 13710
13712	→→¬𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-2
13713	→→¬𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13711, 13712
13714	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌	Modus ponens 13680, 13713
13715	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-3
13716	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Modus ponens 13714, 13715
13717	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌] into ax-1
13718	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Modus ponens 13716, 13717
13719	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜓] into ax-2
13720	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓	Modus ponens 13718, 13719
13721	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓	Modus ponens 13473, 13720
13722	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌] into ax-1
13723	→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓	Modus ponens 13721, 13722
13724	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌𝜓→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗𝜓] into ax-2
13725	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Modus ponens 13723, 13724
13726	→→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓, 𝜓↗𝜌] into ax-1
13727	→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓	Modus ponens 13716, 13726
13728	→→𝜌→¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌𝜓→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓	Subs [𝜑↗𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗𝜓] into ax-2
13729	→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓	Modus ponens 13727, 13728
13730	→→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓	Subs [𝜑↗→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13731	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓	Modus ponens 13729, 13730
13732	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→𝜌𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌, 𝜒↗→𝜌𝜓] into ax-2
13733	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌¬→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁¬𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Modus ponens 13731, 13732
13734	→→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓, 𝜓↗𝜌] into ax-1
13735	→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13646, 13734
13736	→→𝜌→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓] into ax-2
13737	→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜌→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13735, 13736
13738	→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓	Modus ponens 13386, 13737
13739	→→𝜌→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗𝜓] into ax-2
13740	→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Modus ponens 13738, 13739
13741	→→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13742	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓	Modus ponens 13740, 13741
13743	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜌𝜓] into ax-2
13744	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Modus ponens 13742, 13743
13745	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Modus ponens 13512, 13744
13746	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌, 𝜒↗𝜓] into ax-2
13747	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13745, 13746
13748	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗𝜌] into ax-1
13749	→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13747, 13748
13750	→→𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
13751	→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13749, 13750
13752	→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13520, 13751
13753	→→𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Subs [𝜑↗𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
13754	→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Modus ponens 13752, 13753
13755	→→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Subs [𝜑↗→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13756	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Modus ponens 13754, 13755
13757	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜓] into ax-2
13758	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Modus ponens 13756, 13757
13759	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗¬¬𝜌] into ax-1
13760	→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13747, 13759
13761	→→¬¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗¬¬𝜌, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
13762	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13760, 13761
13763	→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13549, 13762
13764	→→¬¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓	Subs [𝜑↗¬¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
13765	→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓	Modus ponens 13763, 13764
13766	→→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓	Subs [𝜑↗→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13767	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓	Modus ponens 13765, 13766
13768	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜌𝜓] into ax-2
13769	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓	Modus ponens 13767, 13768
13770	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓	Modus ponens 13555, 13769
13771	→→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓	Subs [𝜑↗→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13772	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓	Modus ponens 13662, 13771
13773	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌𝜓→¬¬𝜌¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌𝜓, 𝜒↗→¬¬𝜌¬¬𝜓] into ax-2
13774	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓	Modus ponens 13772, 13773
13775	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓	Modus ponens 13770, 13774
13776	→→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌	Subs [𝜑↗→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13777	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌	Modus ponens 13668, 13776
13778	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜌¬¬𝜓→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜌¬¬𝜓, 𝜒↗→¬𝜓¬𝜌] into ax-2
13779	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜌¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌	Modus ponens 13777, 13778
13780	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌	Modus ponens 13775, 13779
13781	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13782	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜓↗¬𝜓] into ax-1
13783	→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓	Modus ponens 13781, 13782
13784	→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓] into ax-2
13785	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓	Modus ponens 13783, 13784
13786	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜓, 𝜒↗¬𝜌] into ax-2
13787	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13780, 13786
13788	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13789	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13787, 13788
13790	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13791	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13789, 13790
13792	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13781, 13791
13793	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13794	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13589, 13793
13795	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13796	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13797	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13795, 13796
13798	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13799	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13797, 13798
13800	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13592, 13799
13801	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13802	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13794, 13801
13803	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13804	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13802, 13803
13805	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13806	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13804, 13805
13807	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-1
13808	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1
13809	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓	Modus ponens 13807, 13808
13810	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓] into ax-2
13811	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓	Modus ponens 13809, 13810
13812	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13813	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13800, 13812
13814	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13815	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13813, 13814
13816	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13817	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13815, 13816
13818	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13807, 13817
13819	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜓↗¬𝜓] into ax-1
13820	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13617, 13819
13821	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13822	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13820, 13821
13823	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13818, 13822
13824	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-2
13825	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13823, 13824
13826	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌	Modus ponens 13792, 13825
13827	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌] into ax-3
13828	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓	Modus ponens 13826, 13827
13829	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13830	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓	Modus ponens 13828, 13829
13831	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌, 𝜒↗𝜓] into ax-2
13832	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 13830, 13831
13833	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 13629, 13832	simp-8r
13834	→→𝜑→𝜎𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑	Subs [𝜑↗→𝜑→𝜎𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
13835	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑	Modus ponens 12918, 13834
13836	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜑→𝜎𝜑→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜓↗𝜑, 𝜒↗→𝜎𝜑] into ax-2
13837	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜑→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜑	Modus ponens 13835, 13836
13838	→𝜑→𝜇𝜑	Subs [𝜓↗𝜇] into ax-1
13839	→→𝜑→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑	Subs [𝜑↗→𝜑→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13840	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑	Modus ponens 13838, 13839
13841	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜑, 𝜒↗→𝜇𝜑] into ax-2
13842	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Modus ponens 13840, 13841
13843	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Modus ponens simp-7l, 13842
13844	↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into df-an
13845	→¬¬𝜇𝜇	Subs [𝜑↗𝜇] into notnotr
13846	→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13847	→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬¬𝜇] into ax-1
13848	→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Modus ponens 13846, 13847
13849	→→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Subs [𝜑↗¬¬𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-2
13850	→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Modus ponens 13848, 13849
13851	→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Modus ponens 13845, 13850
13852	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇, 𝜒↗𝜑] into ax-2
13853	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13843, 13852
13854	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗¬¬𝜇] into ax-1
13855	→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13853, 13854
13856	→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13857	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13855, 13856
13858	→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13851, 13857
13859	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬¬𝜇] into ax-1
13860	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13861	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13859, 13860
13862	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13863	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13861, 13862
13864	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑	Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13865	→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑	Modus ponens 13858, 13864
13866	→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑	Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13867	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑	Modus ponens 13865, 13866
13868	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇𝜑] into ax-2
13869	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑	Modus ponens 13867, 13868
13870	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑	Modus ponens 13859, 13869
13871	→→𝜑¬¬𝜑→¬¬𝜇→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜇] into ax-1
13872	→¬¬𝜇→𝜑¬¬𝜑	Modus ponens notnot, 13871
13873	→→¬¬𝜇→𝜑¬¬𝜑→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑	Subs [𝜑↗¬¬𝜇, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
13874	→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑	Modus ponens 13872, 13873
13875	→→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑	Subs [𝜑↗→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13876	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑	Modus ponens 13874, 13875
13877	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇𝜑, 𝜒↗→¬¬𝜇¬¬𝜑] into ax-2
13878	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑	Modus ponens 13876, 13877
13879	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑	Modus ponens 13870, 13878
13880	→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇	Subs [𝜑↗¬𝜇, 𝜓↗¬𝜑] into ax-3
13881	→→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇	Subs [𝜑↗→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13882	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇	Modus ponens 13880, 13881
13883	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇¬¬𝜑, 𝜒↗→¬𝜑¬𝜇] into ax-2
13884	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇	Modus ponens 13882, 13883
13885	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇	Modus ponens 13879, 13884
13886	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜑, 𝜒↗¬𝜇] into ax-2
13887	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13885, 13886
13888	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13889	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13887, 13888
13890	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13891	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13889, 13890
13892	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13577, 13891
13893	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into id
13894	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13895	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13893, 13894
13896	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into notnotr
13897	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13898	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13899	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13897, 13898
13900	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13901	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13899, 13900
13902	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13896, 13901
13903	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13904	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13895, 13903
13905	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13906	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13904, 13905
13907	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13908	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13906, 13907
13909	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13910	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1
13911	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑	Modus ponens 13909, 13910
13912	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑] into ax-2
13913	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑	Modus ponens 13911, 13912
13914	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13915	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13902, 13914
13916	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13917	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13915, 13916
13918	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13919	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13917, 13918
13920	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13909, 13919
13921	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3
13922	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜑] into ax-1
13923	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13921, 13922
13924	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13925	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13923, 13924
13926	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13920, 13925
13927	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
13928	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13926, 13927
13929	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13892, 13928
13930	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3
13931	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Modus ponens 13929, 13930
13932	→↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into biimp
13933	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13844, 13932
13934	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-1
13935	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Modus ponens 13931, 13934
13936	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜑] into ax-2
13937	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑	Modus ponens 13935, 13936
13938	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑	Modus ponens 13933, 13937
13939	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜌] into simpl
13940	→↔⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into bicom1
13941	↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Modus ponens 13844, 13940
13942	→↔¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into biimp
13943	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Modus ponens 13941, 13942
13944	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
13945	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑	Modus ponens 13938, 13944
13946	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗𝜑] into ax-2
13947	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Modus ponens 13945, 13946
13948	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into pm3.2im
13949	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑, 𝜓↗𝜇] into ax-1
13950	→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑	Modus ponens 13931, 13949
13951	→→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜑→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑	Subs [𝜑↗𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜑] into ax-2
13952	→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑	Modus ponens 13950, 13951
13953	→→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑	Subs [𝜑↗→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
13954	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑	Modus ponens 13952, 13953
13955	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→𝜇𝜑] into ax-2
13956	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Modus ponens 13954, 13955
13957	→𝜇𝜇	Subs [𝜑↗𝜇] into id
13958	→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗𝜇] into ax-1
13959	→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Modus ponens 13846, 13958
13960	→→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Subs [𝜑↗𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-2
13961	→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇	Modus ponens 13959, 13960
13962	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑, 𝜓↗𝜇] into ax-1
13963	→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13853, 13962
13964	→→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑] into ax-2
13965	→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13963, 13964
13966	→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑	Modus ponens 13846, 13965
13967	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇] into ax-1
13968	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13969	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13967, 13968
13970	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-2
13971	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13969, 13970
13972	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎	Modus ponens 13939, 13971
13973	→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜑] into ax-2
13974	→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Modus ponens 13966, 13973
13975	→→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13976	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑	Modus ponens 13974, 13975
13977	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜑] into ax-2
13978	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Modus ponens 13976, 13977
13979	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Modus ponens 13972, 13978
13980	→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13981	→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜇] into ax-1
13982	→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 13980, 13981
13983	→→𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
13984	→→𝜇𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 13982, 13983
13985	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇, 𝜒↗𝜑] into ax-2
13986	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 13979, 13985
13987	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗𝜇] into ax-1
13988	→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 13986, 13987
13989	→→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
13990	→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 13988, 13989
13991	→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 13980, 13990
13992	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into id
13993	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into ax-1
13994	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
13995	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 13993, 13994
13996	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
13997	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 13995, 13996
13998	→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
13999	→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Modus ponens 13991, 13998
14000	→→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14001	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Modus ponens 13999, 14000
14002	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜑] into ax-2
14003	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Modus ponens 14001, 14002
14004	↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into df-an
14005	→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜇] into ax-1
14006	→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 13980, 14005
14007	→→¬¬𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗¬¬𝜇, 𝜓↗𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14008	→→¬¬𝜇𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14006, 14007
14009	→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 13845, 14008
14010	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗¬¬𝜇] into ax-1
14011	→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 13986, 14010
14012	→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
14013	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14011, 14012
14014	→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14009, 14013
14015	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜇] into ax-1
14016	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14017	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 14015, 14016
14018	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
14019	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 14017, 14018
14020	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑	Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
14021	→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑	Modus ponens 14014, 14020
14022	→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑	Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14023	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑	Modus ponens 14021, 14022
14024	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇𝜑] into ax-2
14025	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑	Modus ponens 14023, 14024
14026	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑	Modus ponens 14015, 14025
14027	→→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑	Subs [𝜑↗→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14028	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑	Modus ponens 13874, 14027
14029	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜑→¬¬𝜇¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇𝜑, 𝜒↗→¬¬𝜇¬¬𝜑] into ax-2
14030	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑	Modus ponens 14028, 14029
14031	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑	Modus ponens 14026, 14030
14032	→→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇	Subs [𝜑↗→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14033	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇	Modus ponens 13880, 14032
14034	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜑→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇¬¬𝜑, 𝜒↗→¬𝜑¬𝜇] into ax-2
14035	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇	Modus ponens 14033, 14034
14036	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇	Modus ponens 14031, 14035
14037	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14038	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜓↗¬𝜑] into ax-1
14039	→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑	Modus ponens 14037, 14038
14040	→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑] into ax-2
14041	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑	Modus ponens 14039, 14040
14042	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜑, 𝜒↗¬𝜇] into ax-2
14043	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14036, 14042
14044	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14045	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14043, 14044
14046	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14047	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14045, 14046
14048	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14037, 14047
14049	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into id
14050	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14051	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14049, 14050
14052	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into notnotr
14053	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14054	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14055	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14053, 14054
14056	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14057	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14055, 14056
14058	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14052, 14057
14059	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14060	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14051, 14059
14061	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14062	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14060, 14061
14063	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14064	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14062, 14063
14065	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14066	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1
14067	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑	Modus ponens 14065, 14066
14068	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑] into ax-2
14069	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑	Modus ponens 14067, 14068
14070	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14071	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14058, 14070
14072	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14073	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14071, 14072
14074	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14075	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14073, 14074
14076	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14065, 14075
14077	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3
14078	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜑] into ax-1
14079	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14077, 14078
14080	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14081	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14079, 14080
14082	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14076, 14081
14083	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14084	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14082, 14083
14085	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14048, 14084
14086	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3
14087	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑	Modus ponens 14085, 14086
14088	→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into biimp
14089	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14004, 14088
14090	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14091	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑	Modus ponens 14087, 14090
14092	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗𝜑] into ax-2
14093	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14091, 14092
14094	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14089, 14093	simp-9l
14095	→→𝜓→𝜎𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓	Subs [𝜑↗→𝜓→𝜎𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁] into ax-1
14096	→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓	Modus ponens 13179, 14095
14097	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜓→𝜎𝜓→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁, 𝜒↗→𝜎𝜓] into ax-2
14098	→→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜓→⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁→𝜎𝜓	Modus ponens 14096, 14097
14099	→𝜓→𝜇𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜇] into ax-1
14100	→→𝜓→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓	Subs [𝜑↗→𝜓→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14101	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓	Modus ponens 14099, 14100
14102	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜓] into ax-2
14103	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Modus ponens 14101, 14102
14104	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Modus ponens simp-7r, 14103
14105	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜇, 𝜒↗𝜓] into ax-2
14106	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 14104, 14105
14107	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗¬¬𝜇] into ax-1
14108	→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 14106, 14107
14109	→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
14110	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 14108, 14109
14111	→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13851, 14110
14112	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓	Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
14113	→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓	Modus ponens 14111, 14112
14114	→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓	Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14115	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓	Modus ponens 14113, 14114
14116	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→¬¬𝜇𝜓] into ax-2
14117	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓	Modus ponens 14115, 14116
14118	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓	Modus ponens 13859, 14117
14119	→→𝜓¬¬𝜓→¬¬𝜇→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜇] into ax-1
14120	→¬¬𝜇→𝜓¬¬𝜓	Modus ponens 448, 14119
14121	→→¬¬𝜇→𝜓¬¬𝜓→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓	Subs [𝜑↗¬¬𝜇, 𝜒↗¬¬𝜓] into ax-2
14122	→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓	Modus ponens 14120, 14121
14123	→→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓	Subs [𝜑↗→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14124	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓	Modus ponens 14122, 14123
14125	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇𝜓, 𝜒↗→¬¬𝜇¬¬𝜓] into ax-2
14126	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓	Modus ponens 14124, 14125
14127	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓	Modus ponens 14118, 14126
14128	→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇	Subs [𝜑↗¬𝜇, 𝜓↗¬𝜓] into ax-3
14129	→→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇	Subs [𝜑↗→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14130	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇	Modus ponens 14128, 14129
14131	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→¬¬𝜇¬¬𝜓, 𝜒↗→¬𝜓¬𝜇] into ax-2
14132	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇	Modus ponens 14130, 14131
14133	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇	Modus ponens 14127, 14132
14134	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗¬𝜓, 𝜒↗¬𝜇] into ax-2
14135	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14133, 14134
14136	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14137	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14135, 14136
14138	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14139	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14137, 14138
14140	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13781, 14139
14141	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14142	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13893, 14141
14143	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14144	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14145	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14143, 14144
14146	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14147	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14145, 14146
14148	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13896, 14147
14149	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14150	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14142, 14149
14151	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14152	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14150, 14151
14153	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14154	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14152, 14153
14155	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14156	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1
14157	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓	Modus ponens 14155, 14156
14158	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓] into ax-2
14159	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓	Modus ponens 14157, 14158
14160	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14161	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14148, 14160
14162	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14163	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14161, 14162
14164	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14165	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14163, 14164
14166	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14155, 14165
14167	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗¬𝜓] into ax-1
14168	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 13921, 14167
14169	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14170	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14168, 14169
14171	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14166, 14170
14172	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-2
14173	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14171, 14172
14174	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇	Modus ponens 14140, 14173
14175	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-3
14176	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Modus ponens 14174, 14175
14177	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇] into ax-1
14178	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Modus ponens 14176, 14177
14179	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜓] into ax-2
14180	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓	Modus ponens 14178, 14179
14181	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓	Modus ponens 13933, 14180
14182	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇] into ax-1
14183	→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓	Modus ponens 14181, 14182
14184	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗𝜓] into ax-2
14185	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Modus ponens 14183, 14184
14186	→→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓, 𝜓↗𝜇] into ax-1
14187	→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓	Modus ponens 14176, 14186
14188	→→𝜇→¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇𝜓→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓	Subs [𝜑↗𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗𝜓] into ax-2
14189	→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓	Modus ponens 14187, 14188
14190	→→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓	Subs [𝜑↗→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14191	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓	Modus ponens 14189, 14190
14192	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇, 𝜒↗→𝜇𝜓] into ax-2
14193	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇¬→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎¬𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Modus ponens 14191, 14192
14194	→→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓, 𝜓↗𝜇] into ax-1
14195	→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 14106, 14194
14196	→→𝜇→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓] into ax-2
14197	→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 14195, 14196
14198	→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓	Modus ponens 13846, 14197
14199	→→𝜇→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗𝜓] into ax-2
14200	→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Modus ponens 14198, 14199
14201	→→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14202	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓	Modus ponens 14200, 14201
14203	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜇𝜓] into ax-2
14204	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Modus ponens 14202, 14203
14205	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Modus ponens 13972, 14204
14206	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇, 𝜒↗𝜓] into ax-2
14207	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14205, 14206
14208	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗𝜇] into ax-1
14209	→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14207, 14208
14210	→→𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14211	→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14209, 14210
14212	→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 13980, 14211
14213	→→𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Subs [𝜑↗𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14214	→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Modus ponens 14212, 14213
14215	→→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Subs [𝜑↗→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14216	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Modus ponens 14214, 14215
14217	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜓] into ax-2
14218	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Modus ponens 14216, 14217
14219	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗¬¬𝜇] into ax-1
14220	→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14207, 14219
14221	→→¬¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗¬¬𝜇, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14222	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14220, 14221
14223	→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14009, 14222
14224	→→¬¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓	Subs [𝜑↗¬¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14225	→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓	Modus ponens 14223, 14224
14226	→→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓	Subs [𝜑↗→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14227	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓	Modus ponens 14225, 14226
14228	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜇𝜓] into ax-2
14229	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓	Modus ponens 14227, 14228
14230	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓	Modus ponens 14015, 14229
14231	→→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓	Subs [𝜑↗→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14232	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓	Modus ponens 14122, 14231
14233	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇𝜓→¬¬𝜇¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇𝜓, 𝜒↗→¬¬𝜇¬¬𝜓] into ax-2
14234	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓	Modus ponens 14232, 14233
14235	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓	Modus ponens 14230, 14234
14236	→→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇	Subs [𝜑↗→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14237	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇	Modus ponens 14128, 14236
14238	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜇¬¬𝜓→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜇¬¬𝜓, 𝜒↗→¬𝜓¬𝜇] into ax-2
14239	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜇¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇	Modus ponens 14237, 14238
14240	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇	Modus ponens 14235, 14239
14241	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14242	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜓↗¬𝜓] into ax-1
14243	→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓	Modus ponens 14241, 14242
14244	→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓] into ax-2
14245	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓	Modus ponens 14243, 14244
14246	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜓, 𝜒↗¬𝜇] into ax-2
14247	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14240, 14246
14248	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14249	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14247, 14248
14250	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14251	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14249, 14250
14252	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14241, 14251
14253	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14254	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14049, 14253
14255	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14256	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14257	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14255, 14256
14258	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14259	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14257, 14258
14260	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14052, 14259
14261	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14262	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14254, 14261
14263	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14264	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14262, 14263
14265	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14266	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14264, 14265
14267	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-1
14268	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1
14269	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓	Modus ponens 14267, 14268
14270	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓] into ax-2
14271	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓	Modus ponens 14269, 14270
14272	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14273	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14260, 14272
14274	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14275	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14273, 14274
14276	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14277	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14275, 14276
14278	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14267, 14277
14279	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜓↗¬𝜓] into ax-1
14280	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14077, 14279
14281	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14282	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14280, 14281
14283	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14278, 14282
14284	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-2
14285	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14283, 14284
14286	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇	Modus ponens 14252, 14285
14287	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇] into ax-3
14288	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓	Modus ponens 14286, 14287
14289	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14290	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓	Modus ponens 14288, 14289
14291	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇, 𝜒↗𝜓] into ax-2
14292	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14290, 14291
14293	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14089, 14292	simp-9r
14294	→→𝜑→𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑	Subs [𝜑↗→𝜑→𝜌𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14295	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑	Modus ponens 13378, 14294
14296	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜑→𝜌𝜑→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜓↗𝜑, 𝜒↗→𝜌𝜑] into ax-2
14297	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜑→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜑	Modus ponens 14295, 14296
14298	→𝜑→𝜆𝜑	Subs [𝜓↗𝜆] into ax-1
14299	→→𝜑→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑	Subs [𝜑↗→𝜑→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14300	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑	Modus ponens 14298, 14299
14301	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜑, 𝜒↗→𝜆𝜑] into ax-2
14302	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Modus ponens 14300, 14301
14303	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Modus ponens simp-8l, 14302
14304	↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into df-an
14305	→¬¬𝜆𝜆	Subs [𝜑↗𝜆] into notnotr
14306	→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14307	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬¬𝜆] into ax-1
14308	→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Modus ponens 14306, 14307
14309	→→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Subs [𝜑↗¬¬𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-2
14310	→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Modus ponens 14308, 14309
14311	→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Modus ponens 14305, 14310
14312	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆, 𝜒↗𝜑] into ax-2
14313	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14303, 14312
14314	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗¬¬𝜆] into ax-1
14315	→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14313, 14314
14316	→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
14317	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14315, 14316
14318	→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14311, 14317
14319	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬¬𝜆] into ax-1
14320	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14321	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 14319, 14320
14322	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
14323	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 14321, 14322
14324	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑	Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
14325	→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑	Modus ponens 14318, 14324
14326	→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑	Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14327	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑	Modus ponens 14325, 14326
14328	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆𝜑] into ax-2
14329	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑	Modus ponens 14327, 14328
14330	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑	Modus ponens 14319, 14329
14331	→→𝜑¬¬𝜑→¬¬𝜆→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜆] into ax-1
14332	→¬¬𝜆→𝜑¬¬𝜑	Modus ponens notnot, 14331
14333	→→¬¬𝜆→𝜑¬¬𝜑→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑	Subs [𝜑↗¬¬𝜆, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
14334	→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑	Modus ponens 14332, 14333
14335	→→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑	Subs [𝜑↗→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14336	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑	Modus ponens 14334, 14335
14337	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆𝜑, 𝜒↗→¬¬𝜆¬¬𝜑] into ax-2
14338	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑	Modus ponens 14336, 14337
14339	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑	Modus ponens 14330, 14338
14340	→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆	Subs [𝜑↗¬𝜆, 𝜓↗¬𝜑] into ax-3
14341	→→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆	Subs [𝜑↗→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14342	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆	Modus ponens 14340, 14341
14343	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆¬¬𝜑, 𝜒↗→¬𝜑¬𝜆] into ax-2
14344	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆	Modus ponens 14342, 14343
14345	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆	Modus ponens 14339, 14344
14346	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜑, 𝜒↗¬𝜆] into ax-2
14347	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14345, 14346
14348	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14349	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14347, 14348
14350	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14351	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14349, 14350
14352	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14037, 14351
14353	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into id
14354	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14355	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14353, 14354
14356	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into notnotr
14357	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14358	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14359	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14357, 14358
14360	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14361	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14359, 14360
14362	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14356, 14361
14363	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14364	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14355, 14363
14365	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14366	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14364, 14365
14367	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14368	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14366, 14367
14369	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14370	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1
14371	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑	Modus ponens 14369, 14370
14372	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑] into ax-2
14373	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑	Modus ponens 14371, 14372
14374	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14375	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14362, 14374
14376	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14377	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14375, 14376
14378	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14379	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14377, 14378
14380	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14369, 14379
14381	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3
14382	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜑] into ax-1
14383	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14381, 14382
14384	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14385	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14383, 14384
14386	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14380, 14385
14387	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14388	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14386, 14387
14389	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14352, 14388
14390	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3
14391	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Modus ponens 14389, 14390
14392	→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into biimp
14393	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14304, 14392
14394	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-1
14395	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Modus ponens 14391, 14394
14396	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜑] into ax-2
14397	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑	Modus ponens 14395, 14396
14398	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑	Modus ponens 14393, 14397
14399	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜇] into simpl
14400	→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into bicom1
14401	↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Modus ponens 14304, 14400
14402	→↔¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into biimp
14403	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Modus ponens 14401, 14402
14404	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14405	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑	Modus ponens 14398, 14404
14406	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗𝜑] into ax-2
14407	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Modus ponens 14405, 14406
14408	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into pm3.2im
14409	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑, 𝜓↗𝜆] into ax-1
14410	→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑	Modus ponens 14391, 14409
14411	→→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜑→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑	Subs [𝜑↗𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜑] into ax-2
14412	→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑	Modus ponens 14410, 14411
14413	→→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑	Subs [𝜑↗→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14414	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑	Modus ponens 14412, 14413
14415	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→𝜆𝜑] into ax-2
14416	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Modus ponens 14414, 14415
14417	→𝜆𝜆	Subs [𝜑↗𝜆] into id
14418	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗𝜆] into ax-1
14419	→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Modus ponens 14306, 14418
14420	→→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Subs [𝜑↗𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-2
14421	→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆	Modus ponens 14419, 14420
14422	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑, 𝜓↗𝜆] into ax-1
14423	→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14313, 14422
14424	→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑] into ax-2
14425	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14423, 14424
14426	→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑	Modus ponens 14306, 14425
14427	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆] into ax-1
14428	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14429	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 14427, 14428
14430	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-2
14431	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 14429, 14430
14432	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌	Modus ponens 14399, 14431
14433	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜑] into ax-2
14434	→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Modus ponens 14426, 14433
14435	→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14436	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑	Modus ponens 14434, 14435
14437	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜑] into ax-2
14438	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Modus ponens 14436, 14437
14439	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Modus ponens 14432, 14438
14440	→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14441	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜆] into ax-1
14442	→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14440, 14441
14443	→→𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14444	→→𝜆𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14442, 14443
14445	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆, 𝜒↗𝜑] into ax-2
14446	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14439, 14445
14447	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗𝜆] into ax-1
14448	→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14446, 14447
14449	→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14450	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14448, 14449
14451	→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14440, 14450
14452	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into id
14453	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into ax-1
14454	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14455	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14453, 14454
14456	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14457	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14455, 14456
14458	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14459	→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Modus ponens 14451, 14458
14460	→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14461	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Modus ponens 14459, 14460
14462	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆𝜑] into ax-2
14463	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜑	Modus ponens 14461, 14462
14464	↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into df-an
14465	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬¬𝜆] into ax-1
14466	→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14440, 14465
14467	→→¬¬𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗¬¬𝜆, 𝜓↗𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14468	→→¬¬𝜆𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14466, 14467
14469	→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14305, 14468
14470	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗¬¬𝜆] into ax-1
14471	→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14446, 14470
14472	→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14473	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14471, 14472
14474	→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14469, 14473
14475	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜆] into ax-1
14476	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14477	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14475, 14476
14478	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14479	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14477, 14478
14480	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑	Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14481	→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑	Modus ponens 14474, 14480
14482	→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑	Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14483	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑	Modus ponens 14481, 14482
14484	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆𝜑] into ax-2
14485	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑	Modus ponens 14483, 14484
14486	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑	Modus ponens 14475, 14485
14487	→→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑	Subs [𝜑↗→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14488	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑	Modus ponens 14334, 14487
14489	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜑→¬¬𝜆¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆𝜑, 𝜒↗→¬¬𝜆¬¬𝜑] into ax-2
14490	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑	Modus ponens 14488, 14489
14491	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑	Modus ponens 14486, 14490
14492	→→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆	Subs [𝜑↗→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14493	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆	Modus ponens 14340, 14492
14494	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜑→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆¬¬𝜑, 𝜒↗→¬𝜑¬𝜆] into ax-2
14495	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆	Modus ponens 14493, 14494
14496	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆	Modus ponens 14491, 14495
14497	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14498	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜓↗¬𝜑] into ax-1
14499	→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑	Modus ponens 14497, 14498
14500	→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑] into ax-2
14501	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑	Modus ponens 14499, 14500
14502	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜑, 𝜒↗¬𝜆] into ax-2
14503	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14496, 14502
14504	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14505	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14503, 14504
14506	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14507	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14505, 14506
14508	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14497, 14507
14509	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into id
14510	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14511	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14509, 14510
14512	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into notnotr
14513	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14514	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14515	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14513, 14514
14516	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14517	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14515, 14516
14518	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14512, 14517
14519	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14520	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14511, 14519
14521	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14522	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14520, 14521
14523	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14524	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14522, 14523
14525	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14526	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1
14527	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑	Modus ponens 14525, 14526
14528	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑] into ax-2
14529	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑	Modus ponens 14527, 14528
14530	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14531	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14518, 14530
14532	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14533	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14531, 14532
14534	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14535	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14533, 14534
14536	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14525, 14535
14537	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3
14538	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜑] into ax-1
14539	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14537, 14538
14540	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14541	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14539, 14540
14542	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14536, 14541
14543	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14544	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14542, 14543
14545	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14508, 14544
14546	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3
14547	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑	Modus ponens 14545, 14546
14548	→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into biimp
14549	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14464, 14548
14550	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14551	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑	Modus ponens 14547, 14550
14552	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗𝜑] into ax-2
14553	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14551, 14552
14554	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14549, 14553	simp-10l
14555	→→𝜓→𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓	Subs [𝜑↗→𝜓→𝜌𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎] into ax-1
14556	→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓	Modus ponens 13639, 14555
14557	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜓→𝜌𝜓→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎, 𝜒↗→𝜌𝜓] into ax-2
14558	→→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜓→⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎→𝜌𝜓	Modus ponens 14556, 14557
14559	→𝜓→𝜆𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜆] into ax-1
14560	→→𝜓→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓	Subs [𝜑↗→𝜓→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14561	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓	Modus ponens 14559, 14560
14562	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜓] into ax-2
14563	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Modus ponens 14561, 14562
14564	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Modus ponens simp-8r, 14563
14565	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜆, 𝜒↗𝜓] into ax-2
14566	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14564, 14565
14567	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗¬¬𝜆] into ax-1
14568	→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14566, 14567
14569	→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14570	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14568, 14569
14571	→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14311, 14570
14572	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓	Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14573	→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓	Modus ponens 14571, 14572
14574	→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓	Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14575	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓	Modus ponens 14573, 14574
14576	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→¬¬𝜆𝜓] into ax-2
14577	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓	Modus ponens 14575, 14576
14578	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓	Modus ponens 14319, 14577
14579	→→𝜓¬¬𝜓→¬¬𝜆→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜆] into ax-1
14580	→¬¬𝜆→𝜓¬¬𝜓	Modus ponens 448, 14579
14581	→→¬¬𝜆→𝜓¬¬𝜓→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓	Subs [𝜑↗¬¬𝜆, 𝜒↗¬¬𝜓] into ax-2
14582	→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓	Modus ponens 14580, 14581
14583	→→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓	Subs [𝜑↗→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14584	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓	Modus ponens 14582, 14583
14585	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆𝜓, 𝜒↗→¬¬𝜆¬¬𝜓] into ax-2
14586	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓	Modus ponens 14584, 14585
14587	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓	Modus ponens 14578, 14586
14588	→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆	Subs [𝜑↗¬𝜆, 𝜓↗¬𝜓] into ax-3
14589	→→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆	Subs [𝜑↗→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14590	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆	Modus ponens 14588, 14589
14591	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→¬¬𝜆¬¬𝜓, 𝜒↗→¬𝜓¬𝜆] into ax-2
14592	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆	Modus ponens 14590, 14591
14593	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆	Modus ponens 14587, 14592
14594	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗¬𝜓, 𝜒↗¬𝜆] into ax-2
14595	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14593, 14594
14596	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14597	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14595, 14596
14598	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14599	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14597, 14598
14600	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14241, 14599
14601	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14602	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14353, 14601
14603	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14604	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14605	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14603, 14604
14606	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14607	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14605, 14606
14608	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14356, 14607
14609	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14610	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14602, 14609
14611	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14612	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14610, 14611
14613	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14614	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14612, 14613
14615	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14616	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1
14617	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓	Modus ponens 14615, 14616
14618	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓] into ax-2
14619	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓	Modus ponens 14617, 14618
14620	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14621	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14608, 14620
14622	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14623	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14621, 14622
14624	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14625	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14623, 14624
14626	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14615, 14625
14627	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗¬𝜓] into ax-1
14628	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14381, 14627
14629	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14630	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14628, 14629
14631	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14626, 14630
14632	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-2
14633	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14631, 14632
14634	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆	Modus ponens 14600, 14633
14635	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-3
14636	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Modus ponens 14634, 14635
14637	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆] into ax-1
14638	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Modus ponens 14636, 14637
14639	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜓] into ax-2
14640	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓	Modus ponens 14638, 14639
14641	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓	Modus ponens 14393, 14640
14642	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆] into ax-1
14643	→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓	Modus ponens 14641, 14642
14644	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗𝜓] into ax-2
14645	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Modus ponens 14643, 14644
14646	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓, 𝜓↗𝜆] into ax-1
14647	→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓	Modus ponens 14636, 14646
14648	→→𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆𝜓→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓	Subs [𝜑↗𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗𝜓] into ax-2
14649	→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓	Modus ponens 14647, 14648
14650	→→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓	Subs [𝜑↗→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14651	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓	Modus ponens 14649, 14650
14652	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆, 𝜒↗→𝜆𝜓] into ax-2
14653	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Modus ponens 14651, 14652
14654	→→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓, 𝜓↗𝜆] into ax-1
14655	→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14566, 14654
14656	→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓] into ax-2
14657	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14655, 14656
14658	→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓	Modus ponens 14306, 14657
14659	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗𝜓] into ax-2
14660	→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Modus ponens 14658, 14659
14661	→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14662	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓	Modus ponens 14660, 14661
14663	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜆𝜓] into ax-2
14664	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Modus ponens 14662, 14663
14665	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Modus ponens 14432, 14664
14666	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆, 𝜒↗𝜓] into ax-2
14667	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14665, 14666
14668	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗𝜆] into ax-1
14669	→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14667, 14668
14670	→→𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
14671	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14669, 14670
14672	→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14440, 14671
14673	→→𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Subs [𝜑↗𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
14674	→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Modus ponens 14672, 14673
14675	→→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Subs [𝜑↗→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14676	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Modus ponens 14674, 14675
14677	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜆𝜓] into ax-2
14678	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜆𝜓	Modus ponens 14676, 14677
14679	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗¬¬𝜆] into ax-1
14680	→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14667, 14679
14681	→→¬¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗¬¬𝜆, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
14682	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14680, 14681
14683	→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14469, 14682
14684	→→¬¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓	Subs [𝜑↗¬¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
14685	→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓	Modus ponens 14683, 14684
14686	→→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓	Subs [𝜑↗→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14687	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓	Modus ponens 14685, 14686
14688	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜆𝜓] into ax-2
14689	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓	Modus ponens 14687, 14688
14690	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓	Modus ponens 14475, 14689
14691	→→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓	Subs [𝜑↗→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14692	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓	Modus ponens 14582, 14691
14693	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆𝜓→¬¬𝜆¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆𝜓, 𝜒↗→¬¬𝜆¬¬𝜓] into ax-2
14694	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓	Modus ponens 14692, 14693
14695	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓	Modus ponens 14690, 14694
14696	→→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆	Subs [𝜑↗→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14697	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆	Modus ponens 14588, 14696
14698	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜆¬¬𝜓→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜆¬¬𝜓, 𝜒↗→¬𝜓¬𝜆] into ax-2
14699	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜆¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆	Modus ponens 14697, 14698
14700	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆	Modus ponens 14695, 14699
14701	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14702	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜓↗¬𝜓] into ax-1
14703	→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓	Modus ponens 14701, 14702
14704	→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓] into ax-2
14705	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓	Modus ponens 14703, 14704
14706	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜓, 𝜒↗¬𝜆] into ax-2
14707	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14700, 14706
14708	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14709	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14707, 14708
14710	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14711	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14709, 14710
14712	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14701, 14711
14713	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14714	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14509, 14713
14715	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14716	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14717	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14715, 14716
14718	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14719	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14717, 14718
14720	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14512, 14719
14721	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14722	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14714, 14721
14723	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14724	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14722, 14723
14725	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14726	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14724, 14725
14727	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-1
14728	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1
14729	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓	Modus ponens 14727, 14728
14730	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓] into ax-2
14731	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓	Modus ponens 14729, 14730
14732	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14733	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14720, 14732
14734	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14735	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14733, 14734
14736	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14737	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14735, 14736
14738	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14727, 14737
14739	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜓↗¬𝜓] into ax-1
14740	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14537, 14739
14741	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14742	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14740, 14741
14743	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14738, 14742
14744	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-2
14745	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14743, 14744
14746	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆	Modus ponens 14712, 14745
14747	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆] into ax-3
14748	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓	Modus ponens 14746, 14747
14749	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14750	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓	Modus ponens 14748, 14749
14751	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆, 𝜒↗𝜓] into ax-2
14752	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 14750, 14751
14753	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 14549, 14752	simp-10r
14754	→→𝜑→𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑	Subs [𝜑↗→𝜑→𝜇𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
14755	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑	Modus ponens 13838, 14754
14756	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜑→𝜇𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜓↗𝜑, 𝜒↗→𝜇𝜑] into ax-2
14757	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜑→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜑	Modus ponens 14755, 14756
14758	→𝜑→𝜅𝜑	Subs [𝜓↗𝜅] into ax-1
14759	→→𝜑→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑	Subs [𝜑↗→𝜑→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14760	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑	Modus ponens 14758, 14759
14761	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜑→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜑, 𝜒↗→𝜅𝜑] into ax-2
14762	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Modus ponens 14760, 14761
14763	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Modus ponens simp-9l, 14762
14764	↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into df-an
14765	→¬¬𝜅𝜅	Subs [𝜑↗𝜅] into notnotr
14766	→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14767	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬¬𝜅] into ax-1
14768	→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Modus ponens 14766, 14767
14769	→→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Subs [𝜑↗¬¬𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-2
14770	→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Modus ponens 14768, 14769
14771	→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Modus ponens 14765, 14770
14772	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅, 𝜒↗𝜑] into ax-2
14773	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14763, 14772
14774	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗¬¬𝜅] into ax-1
14775	→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14773, 14774
14776	→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14777	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14775, 14776
14778	→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14771, 14777
14779	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬¬𝜅] into ax-1
14780	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14781	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14779, 14780
14782	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14783	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14781, 14782
14784	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑	Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14785	→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑	Modus ponens 14778, 14784
14786	→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑	Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14787	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑	Modus ponens 14785, 14786
14788	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅𝜑] into ax-2
14789	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑	Modus ponens 14787, 14788
14790	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑	Modus ponens 14779, 14789
14791	→→𝜑¬¬𝜑→¬¬𝜅→𝜑¬¬𝜑	Subs [𝜑↗→𝜑¬¬𝜑, 𝜓↗¬¬𝜅] into ax-1
14792	→¬¬𝜅→𝜑¬¬𝜑	Modus ponens notnot, 14791
14793	→→¬¬𝜅→𝜑¬¬𝜑→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑	Subs [𝜑↗¬¬𝜅, 𝜓↗𝜑, 𝜒↗¬¬𝜑] into ax-2
14794	→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑	Modus ponens 14792, 14793
14795	→→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑	Subs [𝜑↗→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14796	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑	Modus ponens 14794, 14795
14797	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅𝜑, 𝜒↗→¬¬𝜅¬¬𝜑] into ax-2
14798	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑	Modus ponens 14796, 14797
14799	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑	Modus ponens 14790, 14798
14800	→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅	Subs [𝜑↗¬𝜅, 𝜓↗¬𝜑] into ax-3
14801	→→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅	Subs [𝜑↗→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14802	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅	Modus ponens 14800, 14801
14803	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅¬¬𝜑, 𝜒↗→¬𝜑¬𝜅] into ax-2
14804	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅	Modus ponens 14802, 14803
14805	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅	Modus ponens 14799, 14804
14806	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜑, 𝜒↗¬𝜅] into ax-2
14807	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14805, 14806
14808	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14809	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14807, 14808
14810	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14811	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14809, 14810
14812	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14497, 14811
14813	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into id
14814	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14815	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14813, 14814
14816	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into notnotr
14817	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14818	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14819	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14817, 14818
14820	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14821	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14819, 14820
14822	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14816, 14821
14823	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14824	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14815, 14823
14825	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14826	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14824, 14825
14827	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14828	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14826, 14827
14829	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14830	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑, 𝜓↗¬𝜑] into ax-1
14831	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑	Modus ponens 14829, 14830
14832	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑] into ax-2
14833	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑	Modus ponens 14831, 14832
14834	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14835	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14822, 14834
14836	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14837	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14835, 14836
14838	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14839	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14837, 14838
14840	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14829, 14839
14841	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3
14842	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜑] into ax-1
14843	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14841, 14842
14844	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14845	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14843, 14844
14846	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14840, 14845
14847	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
14848	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14846, 14847
14849	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14812, 14848
14850	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3
14851	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Modus ponens 14849, 14850
14852	→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into biimp
14853	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14764, 14852
14854	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-1
14855	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Modus ponens 14851, 14854
14856	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜑] into ax-2
14857	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑	Modus ponens 14855, 14856
14858	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑	Modus ponens 14853, 14857
14859	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜆] into simpl
14860	→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into bicom1
14861	↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Modus ponens 14764, 14860
14862	→↔¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into biimp
14863	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Modus ponens 14861, 14862
14864	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
14865	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑	Modus ponens 14858, 14864
14866	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜑→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗𝜑] into ax-2
14867	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Modus ponens 14865, 14866
14868	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into pm3.2im
14869	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑, 𝜓↗𝜅] into ax-1
14870	→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑	Modus ponens 14851, 14869
14871	→→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜑→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑	Subs [𝜑↗𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜑] into ax-2
14872	→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑	Modus ponens 14870, 14871
14873	→→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑	Subs [𝜑↗→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
14874	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑	Modus ponens 14872, 14873
14875	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→𝜅𝜑] into ax-2
14876	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Modus ponens 14874, 14875
14877	→𝜅𝜅	Subs [𝜑↗𝜅] into id
14878	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗𝜅] into ax-1
14879	→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Modus ponens 14766, 14878
14880	→→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Subs [𝜑↗𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-2
14881	→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅	Modus ponens 14879, 14880
14882	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑, 𝜓↗𝜅] into ax-1
14883	→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14773, 14882
14884	→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑] into ax-2
14885	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14883, 14884
14886	→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑	Modus ponens 14766, 14885
14887	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅] into ax-1
14888	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14889	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14887, 14888
14890	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-2
14891	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14889, 14890
14892	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇	Modus ponens 14859, 14891
14893	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜑→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜑] into ax-2
14894	→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Modus ponens 14886, 14893
14895	→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14896	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑	Modus ponens 14894, 14895
14897	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜑] into ax-2
14898	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Modus ponens 14896, 14897
14899	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Modus ponens 14892, 14898
14900	→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14901	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗𝜅] into ax-1
14902	→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Modus ponens 14900, 14901
14903	→→𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Subs [𝜑↗𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-2
14904	→→𝜅𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Modus ponens 14902, 14903
14905	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅, 𝜒↗𝜑] into ax-2
14906	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14899, 14905
14907	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑, 𝜓↗𝜅] into ax-1
14908	→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14906, 14907
14909	→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑] into ax-2
14910	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14908, 14909
14911	→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14900, 14910
14912	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into id
14913	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅] into ax-1
14914	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14915	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14913, 14914
14916	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14917	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14915, 14916
14918	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜑] into ax-2
14919	→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Modus ponens 14911, 14918
14920	→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14921	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Modus ponens 14919, 14920
14922	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅𝜑] into ax-2
14923	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜑	Modus ponens 14921, 14922
14924	↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅] into df-an
14925	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Subs [𝜑↗→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬¬𝜅] into ax-1
14926	→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Modus ponens 14900, 14925
14927	→→¬¬𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Subs [𝜑↗¬¬𝜅, 𝜓↗𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-2
14928	→→¬¬𝜅𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Modus ponens 14926, 14927
14929	→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅	Modus ponens 14765, 14928
14930	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑, 𝜓↗¬¬𝜅] into ax-1
14931	→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14906, 14930
14932	→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑] into ax-2
14933	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14931, 14932
14934	→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑	Modus ponens 14929, 14933
14935	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬¬𝜅] into ax-1
14936	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14937	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14935, 14936
14938	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-2
14939	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆	Modus ponens 14937, 14938
14940	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜑→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑	Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜑] into ax-2
14941	→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑	Modus ponens 14934, 14940
14942	→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑	Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14943	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑	Modus ponens 14941, 14942
14944	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅𝜑] into ax-2
14945	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑	Modus ponens 14943, 14944
14946	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑	Modus ponens 14935, 14945
14947	→→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑	Subs [𝜑↗→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14948	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑	Modus ponens 14794, 14947
14949	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜑→¬¬𝜅¬¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅𝜑, 𝜒↗→¬¬𝜅¬¬𝜑] into ax-2
14950	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑	Modus ponens 14948, 14949
14951	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑	Modus ponens 14946, 14950
14952	→→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅	Subs [𝜑↗→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14953	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅	Modus ponens 14800, 14952
14954	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜑→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅¬¬𝜑, 𝜒↗→¬𝜑¬𝜅] into ax-2
14955	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅	Modus ponens 14953, 14954
14956	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅	Modus ponens 14951, 14955
14957	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
14958	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑	Subs [𝜑↗→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑, 𝜓↗¬𝜑] into ax-1
14959	→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑	Modus ponens 14957, 14958
14960	→→¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑] into ax-2
14961	→→¬𝜑¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑	Modus ponens 14959, 14960
14962	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜑¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬𝜑, 𝜒↗¬𝜅] into ax-2
14963	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14956, 14962
14964	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14965	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14963, 14964
14966	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14967	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜑→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14965, 14966
14968	→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14957, 14967
14969	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into id
14970	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14971	→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14969, 14970
14972	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into notnotr
14973	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14974	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
14975	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14973, 14974
14976	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14977	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14975, 14976
14978	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14972, 14977
14979	→→¬𝜑→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14980	→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14971, 14979
14981	→→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
14982	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14980, 14981
14983	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14984	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14982, 14983
14985	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
14986	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑, 𝜓↗¬𝜑] into ax-1
14987	→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑	Modus ponens 14985, 14986
14988	→→¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑] into ax-2
14989	→→¬𝜑¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑	Modus ponens 14987, 14988
14990	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14991	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14978, 14990
14992	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14993	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14991, 14992
14994	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
14995	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜑→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14993, 14994
14996	→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14985, 14995
14997	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3
14998	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜑] into ax-1
14999	→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14997, 14998
15000	→→¬𝜑→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15001	→→¬𝜑→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14999, 15000
15002	→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14996, 15001
15003	→→¬𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜑, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15004	→→¬𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15002, 15003
15005	→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14968, 15004
15006	→→¬𝜑¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑	Subs [𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3
15007	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑	Modus ponens 15005, 15006
15008	→↔⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into biimp
15009	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14924, 15008
15010	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-1
15011	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑	Modus ponens 15007, 15010
15012	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜑→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗𝜑] into ax-2
15013	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑	Modus ponens 15011, 15012
15014	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜑	Modus ponens 15009, 15013	simp-11l
15015	→→𝜓→𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓	Subs [𝜑↗→𝜓→𝜇𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌] into ax-1
15016	→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓	Modus ponens 14099, 15015
15017	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜓→𝜇𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌, 𝜒↗→𝜇𝜓] into ax-2
15018	→→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜓→⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌→𝜇𝜓	Modus ponens 15016, 15017
15019	→𝜓→𝜅𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜅] into ax-1
15020	→→𝜓→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓	Subs [𝜑↗→𝜓→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15021	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓	Modus ponens 15019, 15020
15022	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜓→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜓] into ax-2
15023	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Modus ponens 15021, 15022
15024	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Modus ponens simp-9r, 15023
15025	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗𝜅, 𝜒↗𝜓] into ax-2
15026	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 15024, 15025
15027	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗¬¬𝜅] into ax-1
15028	→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 15026, 15027
15029	→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
15030	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 15028, 15029
15031	→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14771, 15030
15032	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓	Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
15033	→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓	Modus ponens 15031, 15032
15034	→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓	Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15035	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓	Modus ponens 15033, 15034
15036	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→¬¬𝜅𝜓] into ax-2
15037	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓	Modus ponens 15035, 15036
15038	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓	Modus ponens 14779, 15037
15039	→→𝜓¬¬𝜓→¬¬𝜅→𝜓¬¬𝜓	Subs [𝜑↗→𝜓¬¬𝜓, 𝜓↗¬¬𝜅] into ax-1
15040	→¬¬𝜅→𝜓¬¬𝜓	Modus ponens 448, 15039
15041	→→¬¬𝜅→𝜓¬¬𝜓→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓	Subs [𝜑↗¬¬𝜅, 𝜒↗¬¬𝜓] into ax-2
15042	→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓	Modus ponens 15040, 15041
15043	→→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓	Subs [𝜑↗→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15044	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓	Modus ponens 15042, 15043
15045	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅𝜓, 𝜒↗→¬¬𝜅¬¬𝜓] into ax-2
15046	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓	Modus ponens 15044, 15045
15047	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓	Modus ponens 15038, 15046
15048	→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅	Subs [𝜑↗¬𝜅, 𝜓↗¬𝜓] into ax-3
15049	→→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅	Subs [𝜑↗→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15050	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅	Modus ponens 15048, 15049
15051	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→¬¬𝜅¬¬𝜓, 𝜒↗→¬𝜓¬𝜅] into ax-2
15052	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅	Modus ponens 15050, 15051
15053	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅	Modus ponens 15047, 15052
15054	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗¬𝜓, 𝜒↗¬𝜅] into ax-2
15055	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15053, 15054
15056	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15057	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15055, 15056
15058	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15059	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15057, 15058
15060	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14701, 15059
15061	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15062	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14813, 15061
15063	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15064	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15065	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15063, 15064
15066	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15067	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15065, 15066
15068	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14816, 15067
15069	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15070	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15062, 15069
15071	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15072	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15070, 15071
15073	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15074	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15072, 15073
15075	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15076	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓, 𝜓↗¬𝜓] into ax-1
15077	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓	Modus ponens 15075, 15076
15078	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓] into ax-2
15079	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓	Modus ponens 15077, 15078
15080	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15081	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15068, 15080
15082	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15083	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15081, 15082
15084	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15085	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15083, 15084
15086	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15075, 15085
15087	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗¬𝜓] into ax-1
15088	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 14841, 15087
15089	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15090	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15088, 15089
15091	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15086, 15090
15092	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-2
15093	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15091, 15092
15094	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅	Modus ponens 15060, 15093
15095	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-3
15096	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Modus ponens 15094, 15095
15097	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅] into ax-1
15098	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Modus ponens 15096, 15097
15099	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜓] into ax-2
15100	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓	Modus ponens 15098, 15099
15101	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓	Modus ponens 14853, 15100
15102	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓	Subs [𝜑↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅] into ax-1
15103	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓	Modus ponens 15101, 15102
15104	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅𝜓→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗𝜓] into ax-2
15105	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Modus ponens 15103, 15104
15106	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓, 𝜓↗𝜅] into ax-1
15107	→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓	Modus ponens 15096, 15106
15108	→→𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅𝜓→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓	Subs [𝜑↗𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗𝜓] into ax-2
15109	→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓	Modus ponens 15107, 15108
15110	→→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓	Subs [𝜑↗→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇] into ax-1
15111	→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓	Modus ponens 15109, 15110
15112	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜓↗→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅, 𝜒↗→𝜅𝜓] into ax-2
15113	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Modus ponens 15111, 15112
15114	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓, 𝜓↗𝜅] into ax-1
15115	→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 15026, 15114
15116	→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓] into ax-2
15117	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 15115, 15116
15118	→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓	Modus ponens 14766, 15117
15119	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜓→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗𝜓] into ax-2
15120	→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Modus ponens 15118, 15119
15121	→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15122	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓	Modus ponens 15120, 15121
15123	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇, 𝜒↗→𝜅𝜓] into ax-2
15124	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Modus ponens 15122, 15123
15125	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Modus ponens 14892, 15124
15126	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗𝜅, 𝜒↗𝜓] into ax-2
15127	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 15125, 15126
15128	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓, 𝜓↗𝜅] into ax-1
15129	→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 15127, 15128
15130	→→𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Subs [𝜑↗𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓] into ax-2
15131	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 15129, 15130
15132	→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 14900, 15131
15133	→→𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Subs [𝜑↗𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜓] into ax-2
15134	→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Modus ponens 15132, 15133
15135	→→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Subs [𝜑↗→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15136	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Modus ponens 15134, 15135
15137	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→𝜅𝜓] into ax-2
15138	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→𝜅𝜓	Modus ponens 15136, 15137
15139	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓, 𝜓↗¬¬𝜅] into ax-1
15140	→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 15127, 15139
15141	→→¬¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Subs [𝜑↗¬¬𝜅, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓] into ax-2
15142	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 15140, 15141
15143	→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓	Modus ponens 14929, 15142
15144	→→¬¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜓→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓	Subs [𝜑↗¬¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗𝜓] into ax-2
15145	→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓	Modus ponens 15143, 15144
15146	→→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓	Subs [𝜑↗→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15147	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓	Modus ponens 15145, 15146
15148	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜒↗→¬¬𝜅𝜓] into ax-2
15149	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓	Modus ponens 15147, 15148
15150	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓	Modus ponens 14935, 15149
15151	→→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓	Subs [𝜑↗→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15152	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓	Modus ponens 15042, 15151
15153	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅𝜓→¬¬𝜅¬¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅𝜓, 𝜒↗→¬¬𝜅¬¬𝜓] into ax-2
15154	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓	Modus ponens 15152, 15153
15155	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓	Modus ponens 15150, 15154
15156	→→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅	Subs [𝜑↗→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15157	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅	Modus ponens 15048, 15156
15158	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→→¬¬𝜅¬¬𝜓→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗→¬¬𝜅¬¬𝜓, 𝜒↗→¬𝜓¬𝜅] into ax-2
15159	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬¬𝜅¬¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅	Modus ponens 15157, 15158
15160	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅	Modus ponens 15155, 15159
15161	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆] into ax-1
15162	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓	Subs [𝜑↗→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓, 𝜓↗¬𝜓] into ax-1
15163	→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓	Modus ponens 15161, 15162
15164	→→¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓] into ax-2
15165	→→¬𝜓¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓	Modus ponens 15163, 15164
15166	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆→¬𝜓¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆, 𝜓↗¬𝜓, 𝜒↗¬𝜅] into ax-2
15167	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15160, 15166
15168	→→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15169	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15167, 15168
15170	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓, 𝜒↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15171	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜓→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15169, 15170
15172	→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15161, 15171
15173	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15174	→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14969, 15173
15175	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15176	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
15177	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15175, 15176
15178	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15179	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15177, 15178
15180	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14972, 15179
15181	→→¬𝜓→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15182	→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15174, 15181
15183	→→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
15184	→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15182, 15183
15185	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15186	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15184, 15185
15187	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-1
15188	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓, 𝜓↗¬𝜓] into ax-1
15189	→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓	Modus ponens 15187, 15188
15190	→→¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓] into ax-2
15191	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓	Modus ponens 15189, 15190
15192	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓, 𝜒↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15193	→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15180, 15192
15194	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15195	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15193, 15194
15196	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓, 𝜒↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15197	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬𝜓→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15195, 15196
15198	→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15187, 15197
15199	→→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜓↗¬𝜓] into ax-1
15200	→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 14997, 15199
15201	→→¬𝜓→→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15202	→→¬𝜓→¬¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15200, 15201
15203	→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15198, 15202
15204	→→¬𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Subs [𝜑↗¬𝜓, 𝜓↗→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-2
15205	→→¬𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15203, 15204
15206	→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅	Modus ponens 15172, 15205
15207	→→¬𝜓¬¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅] into ax-3
15208	→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓	Modus ponens 15206, 15207
15209	→→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓	Subs [𝜑↗→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓, 𝜓↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅] into ax-1
15210	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓	Modus ponens 15208, 15209
15211	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅→¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅𝜓→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓	Subs [𝜑↗⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅, 𝜓↗¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅, 𝜒↗𝜓] into ax-2
15212	→→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅¬→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆¬𝜅→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓	Modus ponens 15210, 15211
15213	→⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀⋀𝜑𝜓𝜒𝜃𝜏𝜂𝜁𝜎𝜌𝜇𝜆𝜅𝜓	Modus ponens 15009, 15212	simp-11r
15214	↔⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜓↗→𝜑𝜓] into df-an
15215	→→𝜑→¬𝜓¬→𝜑𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓	Subs [𝜓↗¬𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
15216	→→𝜑¬𝜓→𝜑¬→𝜑𝜓	Modus ponens jcn, 15215
15217	→→→𝜑¬𝜓→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓	Subs [𝜑↗→→𝜑¬𝜓→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15218	→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓	Modus ponens 15216, 15217
15219	→→¬𝜓→→𝜑¬𝜓→𝜑¬→𝜑𝜓→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬→𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗→𝜑¬→𝜑𝜓] into ax-2
15220	→→¬𝜓→𝜑¬𝜓→¬𝜓→𝜑¬→𝜑𝜓	Modus ponens 15218, 15219
15221	→¬𝜓→𝜑¬→𝜑𝜓	Modus ponens 609, 15220
15222	→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬→𝜑¬→𝜑𝜓] into id
15223	→→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15224	→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15222, 15223
15225	→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬→𝜑¬→𝜑𝜓] into notnotr
15226	→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15227	→→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1
15228	→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15226, 15227
15229	→→¬¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗→¬𝜓¬→𝜑¬→𝜑𝜓] into ax-2
15230	→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15228, 15229
15231	→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15225, 15230
15232	→→¬𝜓→¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗¬→𝜑¬→𝜑𝜓] into ax-2
15233	→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15224, 15232
15234	→→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1
15235	→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15233, 15234
15236	→→¬¬¬→𝜑¬→𝜑𝜓→→¬𝜓¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗→¬𝜓¬→𝜑¬→𝜑𝜓, 𝜒↗→¬𝜓¬→𝜑¬→𝜑𝜓] into ax-2
15237	→→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15235, 15236
15238	→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬¬¬→𝜑¬→𝜑𝜓] into ax-1
15239	→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓	Subs [𝜑↗→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓, 𝜓↗¬𝜓] into ax-1
15240	→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓	Modus ponens 15238, 15239
15241	→→¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬¬¬→𝜑¬→𝜑𝜓¬𝜓] into ax-2
15242	→→¬𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓	Modus ponens 15240, 15241
15243	→→¬¬¬→𝜑¬→𝜑𝜓→¬𝜓¬→𝜑¬→𝜑𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓, 𝜒↗¬→𝜑¬→𝜑𝜓] into ax-2
15244	→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15231, 15243
15245	→→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15246	→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15244, 15245
15247	→→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬→𝜑𝜓¬𝜓, 𝜒↗→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓] into ax-2
15248	→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬𝜓→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15246, 15247
15249	→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15238, 15248
15250	→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬¬→𝜑¬→𝜑𝜓, 𝜓↗→𝜑¬→𝜑𝜓] into ax-3
15251	→→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓, 𝜓↗¬𝜓] into ax-1
15252	→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓	Modus ponens 15250, 15251
15253	→→¬𝜓→→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓, 𝜒↗→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓] into ax-2
15254	→→¬𝜓→¬¬¬→𝜑¬→𝜑𝜓¬→𝜑¬→𝜑𝜓→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓	Modus ponens 15252, 15253
15255	→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓	Modus ponens 15249, 15254
15256	→→¬𝜓→→𝜑¬→𝜑𝜓¬¬→𝜑¬→𝜑𝜓→→¬𝜓→𝜑¬→𝜑𝜓→¬𝜓¬¬→𝜑¬→𝜑𝜓	Subs [𝜑↗¬𝜓, 𝜓↗→𝜑¬→𝜑𝜓, 𝜒↗¬¬→𝜑¬→𝜑𝜓] into ax-2
15257	→→¬𝜓→𝜑¬→𝜑𝜓→¬𝜓¬¬→𝜑¬→𝜑𝜓	Modus ponens 15255, 15256
15258	→¬𝜓¬¬→𝜑¬→𝜑𝜓	Modus ponens 15221, 15257
15259	→→¬𝜓¬¬→𝜑¬→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓] into ax-3
15260	→¬→𝜑¬→𝜑𝜓𝜓	Modus ponens 15258, 15259
15261	→↔⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓	Subs [𝜑↗⋀𝜑→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓] into biimp
15262	→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓	Modus ponens 15214, 15261
15263	→→¬→𝜑¬→𝜑𝜓𝜓→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓	Subs [𝜑↗→¬→𝜑¬→𝜑𝜓𝜓, 𝜓↗⋀𝜑→𝜑𝜓] into ax-1
15264	→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓	Modus ponens 15260, 15263
15265	→→⋀𝜑→𝜑𝜓→¬→𝜑¬→𝜑𝜓𝜓→→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑→𝜑𝜓, 𝜓↗¬→𝜑¬→𝜑𝜓, 𝜒↗𝜓] into ax-2
15266	→→⋀𝜑→𝜑𝜓¬→𝜑¬→𝜑𝜓→⋀𝜑→𝜑𝜓𝜓	Modus ponens 15264, 15265
15267	→⋀𝜑→𝜑𝜓𝜓	Modus ponens 15262, 15266	pm3.35
15268	→↔𝜓𝜒↔𝜓𝜒	Subs [𝜑↗↔𝜓𝜒] into id
15269	↔↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into bicom
15270	→↔↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔↔𝜑𝜒↔𝜓𝜒, 𝜓↗↔↔𝜓𝜒↔𝜑𝜒] into biimp
15271	→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒	Modus ponens 15269, 15270
15272	→→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15273	→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒	Modus ponens 15271, 15272
15274	→→↔𝜑𝜓→↔↔𝜑𝜒↔𝜓𝜒↔↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜑𝜒↔𝜓𝜒, 𝜒↗↔↔𝜓𝜒↔𝜑𝜒] into ax-2
15275	→→↔𝜑𝜓↔↔𝜑𝜒↔𝜓𝜒→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒	Modus ponens 15273, 15274
15276	→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒	Modus ponens bibi1, 15275
15277	→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜒] into biimp
15278	→→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15279	→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒	Modus ponens 15277, 15278
15280	→→↔𝜑𝜓→↔↔𝜓𝜒↔𝜑𝜒→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔↔𝜓𝜒↔𝜑𝜒, 𝜒↗→↔𝜓𝜒↔𝜑𝜒] into ax-2
15281	→→↔𝜑𝜓↔↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Modus ponens 15279, 15280
15282	→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Modus ponens 15276, 15281
15283	→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15284	→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗↔𝜓𝜒] into ax-1
15285	→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 15283, 15284
15286	→→↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→→↔𝜓𝜒↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2
15287	→→↔𝜓𝜒↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 15285, 15286
15288	→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒, 𝜒↗↔𝜑𝜒] into ax-2
15289	→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜓𝜒] into ax-1
15290	→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2744, 15289
15291	→→↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15292	→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15290, 15291
15293	→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15283, 15292
15294	→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒] into ax-1
15295	→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15296	→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓	Modus ponens 15294, 15295
15297	→→↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜓𝜒↔𝜑𝜓] into ax-2
15298	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓	Modus ponens 15296, 15297
15299	→→↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜓𝜒, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15300	→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Modus ponens 15293, 15299
15301	→→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15302	→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Modus ponens 15300, 15301
15303	→→↔𝜑𝜓→→↔𝜓𝜒↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜓𝜒↔𝜑𝜓, 𝜒↗→↔𝜓𝜒↔𝜑𝜒] into ax-2
15304	→→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜓𝜒↔𝜑𝜒	Modus ponens 15302, 15303
15305	↔⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜓𝜒] into df-an
15306	→¬¬↔𝜓𝜒↔𝜓𝜒	Subs [𝜑↗↔𝜓𝜒] into notnotr
15307	→→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15308	→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 15283, 15307
15309	→→¬¬↔𝜓𝜒→↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→→¬¬↔𝜓𝜒↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜓𝜒] into ax-2
15310	→→¬¬↔𝜓𝜒↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 15308, 15309
15311	→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒	Modus ponens 15306, 15310
15312	→→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15313	→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2744, 15312
15314	→→¬¬↔𝜓𝜒→→↔𝜑𝜓↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗→↔𝜑𝜓↔𝜓𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15315	→→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜓𝜒→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15313, 15314
15316	→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15311, 15315
15317	→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15318	→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15319	→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓	Modus ponens 15317, 15318
15320	→→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬↔𝜓𝜒↔𝜑𝜓] into ax-2
15321	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓	Modus ponens 15319, 15320
15322	→→¬¬↔𝜓𝜒→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15323	→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒	Modus ponens 15316, 15322
15324	→→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15325	→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒	Modus ponens 15323, 15324
15326	→→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒↔𝜑𝜓, 𝜒↗→¬¬↔𝜓𝜒↔𝜑𝜒] into ax-2
15327	→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒	Modus ponens 15325, 15326
15328	→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒	Modus ponens 15317, 15327
15329	→↔𝜑𝜒¬¬↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜒] into notnot
15330	→→↔𝜑𝜒¬¬↔𝜑𝜒→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜒¬¬↔𝜑𝜒, 𝜓↗¬¬↔𝜓𝜒] into ax-1
15331	→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒	Modus ponens 15329, 15330
15332	→→¬¬↔𝜓𝜒→↔𝜑𝜒¬¬↔𝜑𝜒→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒	Subs [𝜑↗¬¬↔𝜓𝜒, 𝜓↗↔𝜑𝜒, 𝜒↗¬¬↔𝜑𝜒] into ax-2
15333	→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒	Modus ponens 15331, 15332
15334	→→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒	Subs [𝜑↗→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15335	→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒	Modus ponens 15333, 15334
15336	→→↔𝜑𝜓→→¬¬↔𝜓𝜒↔𝜑𝜒→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒↔𝜑𝜒, 𝜒↗→¬¬↔𝜓𝜒¬¬↔𝜑𝜒] into ax-2
15337	→→↔𝜑𝜓→¬¬↔𝜓𝜒↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒	Modus ponens 15335, 15336
15338	→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒	Modus ponens 15328, 15337
15339	→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒	Subs [𝜑↗¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-3
15340	→→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒	Subs [𝜑↗→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15341	→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒	Modus ponens 15339, 15340
15342	→→↔𝜑𝜓→→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜓𝜒→→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜓𝜒¬¬↔𝜑𝜒, 𝜒↗→¬↔𝜑𝜒¬↔𝜓𝜒] into ax-2
15343	→→↔𝜑𝜓→¬¬↔𝜓𝜒¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒	Modus ponens 15341, 15342
15344	→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒	Modus ponens 15338, 15343
15345	→¬↔𝜑𝜒¬↔𝜑𝜒	Subs [𝜑↗¬↔𝜑𝜒] into id
15346	→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15347	→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒	Subs [𝜑↗→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15348	→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒	Modus ponens 15346, 15347
15349	→→¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜑𝜒] into ax-2
15350	→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒	Modus ponens 15348, 15349
15351	→→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬↔𝜓𝜒] into ax-2
15352	→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15344, 15351
15353	→→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15354	→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15352, 15353
15355	→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15356	→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15354, 15355
15357	→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15346, 15356
15358	→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒] into id
15359	→→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15360	→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15358, 15359
15361	→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒] into notnotr
15362	→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15363	→→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1
15364	→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15362, 15363
15365	→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15366	→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15364, 15365
15367	→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15361, 15366
15368	→→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15369	→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15360, 15368
15370	→→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1
15371	→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15369, 15370
15372	→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15373	→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15371, 15372
15374	→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-1
15375	→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒	Subs [𝜑↗→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15376	→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒	Modus ponens 15374, 15375
15377	→→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒] into ax-2
15378	→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒	Modus ponens 15376, 15377
15379	→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15380	→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15367, 15379
15381	→→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15382	→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15380, 15381
15383	→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15384	→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15382, 15383
15385	→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15374, 15384
15386	→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜓𝜒] into ax-3
15387	→→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15388	→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15386, 15387
15389	→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15390	→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15388, 15389
15391	→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15385, 15390
15392	→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜓𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗¬¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-2
15393	→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜓𝜒→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15391, 15392
15394	→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15357, 15393
15395	→→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒] into ax-3
15396	→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒	Modus ponens 15394, 15395
15397	→↔⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Subs [𝜑↗⋀↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒] into biimp
15398	→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒	Modus ponens 15305, 15397
15399	→→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜓↔𝜓𝜒] into ax-1
15400	→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒	Modus ponens 15396, 15399
15401	→→⋀↔𝜑𝜓↔𝜓𝜒→¬→↔𝜑𝜓¬↔𝜓𝜒↔𝜑𝜒→→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒	Subs [𝜑↗⋀↔𝜑𝜓↔𝜓𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜓𝜒, 𝜒↗↔𝜑𝜒] into ax-2
15402	→→⋀↔𝜑𝜓↔𝜓𝜒¬→↔𝜑𝜓¬↔𝜓𝜒→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒	Modus ponens 15400, 15401
15403	→⋀↔𝜑𝜓↔𝜓𝜒↔𝜑𝜒	Modus ponens 15398, 15402	bitr
15404	→↔𝜒𝜓↔𝜒𝜓	Subs [𝜑↗↔𝜒𝜓] into id
15405	↔→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into pm5.74
15406	→↔→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗→↔𝜒𝜓↔𝜒𝜓, 𝜓↗↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp
15407	→→↔𝜒𝜓↔𝜒𝜓↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15405, 15406
15408	↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15404, 15407
15409	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into id
15410	→↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-1
15411	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15408, 15410
15412	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74
15413	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp
15414	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Modus ponens 15412, 15413
15415	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Modus ponens 15409, 15414
15416	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74
15417	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp
15418	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15416, 15417
15419	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15411, 15418
15420	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into biimp
15421	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15419, 15420
15422	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp
15423	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Modus ponens 15415, 15422
15424	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into ax-1
15425	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15421, 15424
15426	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into ax-2
15427	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15425, 15426
15428	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15423, 15427
15429	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into bicom1
15430	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Modus ponens 15419, 15429
15431	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into biimp
15432	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒	Modus ponens 15430, 15431
15433	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒] into bicom1
15434	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Modus ponens 15415, 15433
15435	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into biimp
15436	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Modus ponens 15434, 15435
15437	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into ax-1
15438	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Modus ponens 15436, 15437
15439	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑] into ax-2
15440	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Modus ponens 15438, 15439
15441	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑	Modus ponens 15432, 15440
15442	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into impbi
15443	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15428, 15442
15444	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Modus ponens 15441, 15443
15445	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74
15446	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓] into bicom1
15447	↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Modus ponens 15445, 15446
15448	→↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp
15449	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Modus ponens 15447, 15448
15450	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Modus ponens 15444, 15449
15451	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into id
15452	→↔→↔𝜒𝜓𝜒→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓𝜓] into bicom1
15453	↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15408, 15452
15454	→↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into ax-1
15455	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15453, 15454
15456	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜓] into pm5.74
15457	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp
15458	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Modus ponens 15456, 15457
15459	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Modus ponens 15451, 15458
15460	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜓, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74
15461	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into biimp
15462	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15460, 15461
15463	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15455, 15462
15464	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into biimp
15465	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15463, 15464
15466	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp
15467	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Modus ponens 15459, 15466
15468	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into ax-1
15469	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15465, 15468
15470	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into ax-2
15471	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15469, 15470
15472	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15467, 15471
15473	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into bicom1
15474	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Modus ponens 15463, 15473
15475	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into biimp
15476	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓	Modus ponens 15474, 15475
15477	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓] into bicom1
15478	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Modus ponens 15459, 15477
15479	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into biimp
15480	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Modus ponens 15478, 15479
15481	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Subs [𝜑↗→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into ax-1
15482	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Modus ponens 15480, 15481
15483	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓, 𝜒↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑] into ax-2
15484	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Modus ponens 15482, 15483
15485	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑	Modus ponens 15476, 15484
15486	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into impbi
15487	→→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15472, 15486
15488	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Modus ponens 15485, 15487
15489	↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓𝜑, 𝜒↗→↔𝜒𝜓𝜒] into pm5.74
15490	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒] into bicom1
15491	↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15489, 15490
15492	→↔↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒, 𝜓↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15493	→↔→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜑→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15491, 15492
15494	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15488, 15493
15495	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into impbi
15496	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Modus ponens 15450, 15495
15497	↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Modus ponens 15494, 15496
15498	↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜑] into pm5.74
15499	↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗↔𝜒𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.74
15500	→↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into bicom1
15501	↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15499, 15500
15502	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into biimp
15503	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15501, 15502
15504	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp
15505	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-1
15506	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15503, 15505
15507	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2
15508	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15506, 15507
15509	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15450, 15508
15510	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into bicom1
15511	→↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into biimp
15512	→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓	Modus ponens 15499, 15511
15513	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓] into bicom1
15514	↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15497, 15513
15515	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15516	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into ax-1
15517	→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15494, 15516
15518	→→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓, 𝜒↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into ax-2
15519	→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜓→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15517, 15518
15520	→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15512, 15519
15521	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into impbi
15522	→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15509, 15521
15523	↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15520, 15522
15524	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into biimp
15525	→↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15526	→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15498, 15525
15527	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜒] into ax-1
15528	→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15509, 15527
15529	→→→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2
15530	→→→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15528, 15529
15531	→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15526, 15530
15532	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into bicom1
15533	↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Modus ponens 15523, 15532
15534	→↔→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into biimp
15535	→↔→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒] into bicom1
15536	↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15498, 15535
15537	→↔↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜒] into biimp
15538	→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15536, 15537
15539	→→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into ax-1
15540	→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15538, 15539
15541	→→→↔𝜒𝜓↔𝜑𝜓→↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→↔𝜒𝜓↔𝜑𝜒→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒, 𝜒↗→↔𝜒𝜓↔𝜑𝜒] into ax-2
15542	→→→↔𝜒𝜓↔𝜑𝜓↔→↔𝜒𝜓𝜑→↔𝜒𝜓𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15540, 15541
15543	→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15520, 15542
15544	→→→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜒𝜓↔𝜑𝜒, 𝜓↗→↔𝜒𝜓↔𝜑𝜓] into impbi
15545	→→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15531, 15544
15546	↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15543, 15545
15547	↔→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗↔𝜑𝜓] into pm5.74
15548	→↔→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓	Subs [𝜑↗→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓] into bicom1
15549	↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓	Modus ponens 15547, 15548
15550	→↔↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓	Subs [𝜑↗↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓] into biimp
15551	→↔→↔𝜒𝜓↔𝜑𝜒→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓	Modus ponens 15549, 15550
15552	→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓	Modus ponens 15546, 15551
15553	↔↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into bicom
15554	→↔↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑𝜒↔𝜑𝜓, 𝜓↗↔↔𝜑𝜓↔𝜑𝜒] into biimp
15555	→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒	Modus ponens 15553, 15554
15556	→→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1
15557	→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒	Modus ponens 15555, 15556
15558	→→↔𝜒𝜓→↔↔𝜑𝜒↔𝜑𝜓↔↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔↔𝜑𝜒↔𝜑𝜓, 𝜒↗↔↔𝜑𝜓↔𝜑𝜒] into ax-2
15559	→→↔𝜒𝜓↔↔𝜑𝜒↔𝜑𝜓→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒	Modus ponens 15557, 15558
15560	→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒	Modus ponens 15552, 15559
15561	→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜒] into biimp
15562	→→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1
15563	→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15561, 15562
15564	→→↔𝜒𝜓→↔↔𝜑𝜓↔𝜑𝜒→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔↔𝜑𝜓↔𝜑𝜒, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15565	→→↔𝜒𝜓↔↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15563, 15564
15566	→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15560, 15565
15567	→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓] into ax-1
15568	→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15569	→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15567, 15568
15570	→→↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜓] into ax-2
15571	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓	Modus ponens 15569, 15570
15572	→→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15573	→→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15574	→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15543, 15573
15575	→→↔𝜑𝜓→→↔𝜒𝜓↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→↔𝜒𝜓↔𝜑𝜓, 𝜒↗→↔𝜒𝜓↔𝜑𝜒] into ax-2
15576	→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15574, 15575
15577	→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒	Modus ponens 15567, 15576
15578	→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15579	→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗↔𝜒𝜓] into ax-1
15580	→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 15578, 15579
15581	→→↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→→↔𝜒𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗↔𝜒𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
15582	→→↔𝜒𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 15580, 15581
15583	→→↔𝜑𝜓→↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15584	→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗↔𝜒𝜓] into ax-1
15585	→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2705, 15584
15586	→→↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15587	→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15585, 15586
15588	↔⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜒𝜓] into df-an
15589	→¬¬↔𝜒𝜓↔𝜒𝜓	Subs [𝜑↗↔𝜒𝜓] into notnotr
15590	→→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15591	→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 15578, 15590
15592	→→¬¬↔𝜒𝜓→↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→→¬¬↔𝜒𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜒𝜓] into ax-2
15593	→→¬¬↔𝜒𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 15591, 15592
15594	→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓	Modus ponens 15589, 15593
15595	→→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15596	→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 2705, 15595
15597	→→¬¬↔𝜒𝜓→→↔𝜑𝜓↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗→↔𝜑𝜓↔𝜒𝜓, 𝜒↗→↔𝜑𝜓↔𝜑𝜒] into ax-2
15598	→→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜒𝜓→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15596, 15597
15599	→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒	Modus ponens 15594, 15598
15600	→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15601	→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15602	→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓	Modus ponens 15600, 15601
15603	→→↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗→¬¬↔𝜒𝜓↔𝜑𝜓] into ax-2
15604	→→↔𝜑𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓	Modus ponens 15602, 15603
15605	→→¬¬↔𝜒𝜓→↔𝜑𝜓↔𝜑𝜒→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15606	→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒	Modus ponens 15599, 15605
15607	→→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15608	→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒	Modus ponens 15606, 15607
15609	→→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓↔𝜑𝜓, 𝜒↗→¬¬↔𝜒𝜓↔𝜑𝜒] into ax-2
15610	→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜓→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒	Modus ponens 15608, 15609
15611	→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒	Modus ponens 15600, 15610
15612	→→↔𝜑𝜒¬¬↔𝜑𝜒→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒	Subs [𝜑↗→↔𝜑𝜒¬¬↔𝜑𝜒, 𝜓↗¬¬↔𝜒𝜓] into ax-1
15613	→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒	Modus ponens 15329, 15612
15614	→→¬¬↔𝜒𝜓→↔𝜑𝜒¬¬↔𝜑𝜒→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒	Subs [𝜑↗¬¬↔𝜒𝜓, 𝜓↗↔𝜑𝜒, 𝜒↗¬¬↔𝜑𝜒] into ax-2
15615	→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒	Modus ponens 15613, 15614
15616	→→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒	Subs [𝜑↗→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒, 𝜓↗↔𝜑𝜓] into ax-1
15617	→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒	Modus ponens 15615, 15616
15618	→→↔𝜑𝜓→→¬¬↔𝜒𝜓↔𝜑𝜒→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓↔𝜑𝜒, 𝜒↗→¬¬↔𝜒𝜓¬¬↔𝜑𝜒] into ax-2
15619	→→↔𝜑𝜓→¬¬↔𝜒𝜓↔𝜑𝜒→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒	Modus ponens 15617, 15618
15620	→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒	Modus ponens 15611, 15619
15621	→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓	Subs [𝜑↗¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-3
15622	→→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓	Subs [𝜑↗→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓, 𝜓↗↔𝜑𝜓] into ax-1
15623	→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓	Modus ponens 15621, 15622
15624	→→↔𝜑𝜓→→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→¬↔𝜑𝜒¬↔𝜒𝜓→→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗→¬¬↔𝜒𝜓¬¬↔𝜑𝜒, 𝜒↗→¬↔𝜑𝜒¬↔𝜒𝜓] into ax-2
15625	→→↔𝜑𝜓→¬¬↔𝜒𝜓¬¬↔𝜑𝜒→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓	Modus ponens 15623, 15624
15626	→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓	Modus ponens 15620, 15625
15627	→→↔𝜑𝜓→¬↔𝜑𝜒¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬↔𝜒𝜓] into ax-2
15628	→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15626, 15627
15629	→→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15630	→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15628, 15629
15631	→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜑𝜒, 𝜒↗→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15632	→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15630, 15631
15633	→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15346, 15632
15634	→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓] into id
15635	→→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15636	→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15634, 15635
15637	→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓] into notnotr
15638	→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15639	→→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1
15640	→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15638, 15639
15641	→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15642	→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15640, 15641
15643	→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15637, 15642
15644	→→¬↔𝜑𝜒→¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15645	→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15636, 15644
15646	→→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1
15647	→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15645, 15646
15648	→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15649	→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15647, 15648
15650	→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-1
15651	→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒	Subs [𝜑↗→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒] into ax-1
15652	→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒	Modus ponens 15650, 15651
15653	→→¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒] into ax-2
15654	→→¬↔𝜑𝜒¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒	Modus ponens 15652, 15653
15655	→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬→↔𝜑𝜓¬↔𝜒𝜓→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒, 𝜒↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15656	→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15643, 15655
15657	→→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15658	→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15656, 15657
15659	→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒, 𝜒↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15660	→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬↔𝜑𝜒→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15658, 15659
15661	→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15650, 15660
15662	→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗→↔𝜑𝜓¬↔𝜒𝜓] into ax-3
15663	→→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜓↗¬↔𝜑𝜒] into ax-1
15664	→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15662, 15663
15665	→→¬↔𝜑𝜒→→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15666	→→¬↔𝜑𝜒→¬¬¬→↔𝜑𝜓¬↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15664, 15665
15667	→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15661, 15666
15668	→→¬↔𝜑𝜒→→↔𝜑𝜓¬↔𝜒𝜓¬¬→↔𝜑𝜓¬↔𝜒𝜓→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗¬↔𝜑𝜒, 𝜓↗→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗¬¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-2
15669	→→¬↔𝜑𝜒→↔𝜑𝜓¬↔𝜒𝜓→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15667, 15668
15670	→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15633, 15669
15671	→→¬↔𝜑𝜒¬¬→↔𝜑𝜓¬↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗↔𝜑𝜒, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓] into ax-3
15672	→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒	Modus ponens 15670, 15671
15673	→↔⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Subs [𝜑↗⋀↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓] into biimp
15674	→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓	Modus ponens 15588, 15673
15675	→→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒, 𝜓↗⋀↔𝜑𝜓↔𝜒𝜓] into ax-1
15676	→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒	Modus ponens 15672, 15675
15677	→→⋀↔𝜑𝜓↔𝜒𝜓→¬→↔𝜑𝜓¬↔𝜒𝜓↔𝜑𝜒→→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒	Subs [𝜑↗⋀↔𝜑𝜓↔𝜒𝜓, 𝜓↗¬→↔𝜑𝜓¬↔𝜒𝜓, 𝜒↗↔𝜑𝜒] into ax-2
15678	→→⋀↔𝜑𝜓↔𝜒𝜓¬→↔𝜑𝜓¬↔𝜒𝜓→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒	Modus ponens 15676, 15677
15679	→⋀↔𝜑𝜓↔𝜒𝜓↔𝜑𝜒	Modus ponens 15674, 15678	biantr
15680	↔→𝜓𝜒→¬𝜒¬𝜓	Subs [𝜑↗𝜓, 𝜓↗𝜒] into con34b
15681	→↔→𝜓𝜒→¬𝜒¬𝜓→𝜑↔→𝜓𝜒→¬𝜒¬𝜓	Subs [𝜑↗↔→𝜓𝜒→¬𝜒¬𝜓, 𝜓↗𝜑] into ax-1
15682	→𝜑↔→𝜓𝜒→¬𝜒¬𝜓	Modus ponens 15680, 15681
15683	↔→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓	Subs [𝜓↗→𝜓𝜒, 𝜒↗→¬𝜒¬𝜓] into pm5.74
15684	→↔→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓	Subs [𝜑↗→𝜑↔→𝜓𝜒→¬𝜒¬𝜓, 𝜓↗↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓] into biimp
15685	→→𝜑↔→𝜓𝜒→¬𝜒¬𝜓↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓	Modus ponens 15683, 15684
15686	↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓	Modus ponens 15682, 15685
15687	↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓	Subs [𝜓↗¬𝜒, 𝜒↗¬𝜓] into impexp
15688	→↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓] into bicom1
15689	↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓	Modus ponens 15687, 15688
15690	→↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp
15691	→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓	Modus ponens 15689, 15690
15692	→↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓] into biimp
15693	→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓	Modus ponens 15686, 15692
15694	→→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into ax-1
15695	→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓	Modus ponens 15691, 15694
15696	→→→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓→→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓, 𝜒↗→⋀𝜑¬𝜒¬𝜓] into ax-2
15697	→→→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens 15695, 15696
15698	→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens 15693, 15697
15699	→↔→𝜑→¬𝜒¬𝜓→⋀𝜑¬𝜒¬𝜓↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓	Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into bicom1
15700	→↔→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓	Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓] into biimp
15701	→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓	Modus ponens 15687, 15700
15702	→↔→𝜑→𝜓𝜒→𝜑→¬𝜒¬𝜓↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→𝜑→¬𝜒¬𝜓] into bicom1
15703	↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒	Modus ponens 15686, 15702
15704	→↔→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into biimp
15705	→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒	Modus ponens 15703, 15704
15706	→→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into ax-1
15707	→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒	Modus ponens 15705, 15706
15708	→→→⋀𝜑¬𝜒¬𝜓→→𝜑→¬𝜒¬𝜓→𝜑→𝜓𝜒→→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→¬𝜒¬𝜓, 𝜒↗→𝜑→𝜓𝜒] into ax-2
15709	→→→⋀𝜑¬𝜒¬𝜓→𝜑→¬𝜒¬𝜓→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒	Modus ponens 15707, 15708
15710	→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒	Modus ponens 15701, 15709
15711	→→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into impbi
15712	→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens 15698, 15711
15713	↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens 15710, 15712
15714	→↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp
15715	→↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into biimp
15716	→→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
15717	→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens 15698, 15716
15718	→→→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑¬𝜒¬𝜓] into ax-2
15719	→→→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens 15717, 15718
15720	→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens pm3.3, 15719	pm3.37
15721	→↔→𝜑→𝜓𝜒→⋀𝜑¬𝜒¬𝜓↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into bicom1
15722	↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒	Modus ponens 15713, 15721
15723	→↔→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒	Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒] into biimp
15724	→↔→⋀𝜑𝜓𝜒→𝜑→𝜓𝜒↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→𝜓𝜒] into bicom1
15725	↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens impexp, 15724
15726	→↔→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜑→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into biimp
15727	→→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into ax-1
15728	→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens pm3.31, 15727
15729	→→→⋀𝜑¬𝜒¬𝜓→→𝜑→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒	Subs [𝜑↗→⋀𝜑¬𝜒¬𝜓, 𝜓↗→𝜑→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
15730	→→→⋀𝜑¬𝜒¬𝜓→𝜑→𝜓𝜒→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒	Modus ponens 15728, 15729
15731	→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒	Modus ponens 15710, 15730
15732	→→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into impbi
15733	→→→⋀𝜑¬𝜒¬𝜓→⋀𝜑𝜓𝜒↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens pm3.37, 15732
15734	↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Modus ponens 15731, 15733	pm4.14
15735	→↔→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓→→⋀𝜑𝜓𝜒→⋀𝜑¬𝜒¬𝜓	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑¬𝜒¬𝜓] into biimp
15736	→→𝜒𝜃→𝜒𝜃	Subs [𝜑↗→𝜒𝜃] into id
15737	→→𝜑→→𝜑𝜓𝜑→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑	Subs [𝜑↗→𝜑→→𝜑𝜓𝜑, 𝜓↗⋀𝜑𝜒] into ax-1
15738	→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑	Modus ponens 25, 15737
15739	→→⋀𝜑𝜒→𝜑→→𝜑𝜓𝜑→→⋀𝜑𝜒𝜑→⋀𝜑𝜒→→𝜑𝜓𝜑	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗𝜑, 𝜒↗→→𝜑𝜓𝜑] into ax-2
15740	→→⋀𝜑𝜒𝜑→⋀𝜑𝜒→→𝜑𝜓𝜑	Modus ponens 15738, 15739
15741	→⋀𝜑𝜒→→𝜑𝜓𝜑	Modus ponens 8604, 15740
15742	→→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Subs [𝜑↗→→→𝜑𝜓𝜑→→𝜑𝜓𝜓, 𝜓↗⋀𝜑𝜒] into ax-1
15743	→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓	Modus ponens 31, 15742
15744	→→⋀𝜑𝜒→→→𝜑𝜓𝜑→→𝜑𝜓𝜓→→⋀𝜑𝜒→→𝜑𝜓𝜑→⋀𝜑𝜒→→𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→→𝜑𝜓𝜑, 𝜒↗→→𝜑𝜓𝜓] into ax-2
15745	→→⋀𝜑𝜒→→𝜑𝜓𝜑→⋀𝜑𝜒→→𝜑𝜓𝜓	Modus ponens 15743, 15744
15746	→⋀𝜑𝜒→→𝜑𝜓𝜓	Modus ponens 15741, 15745
15747	→→⋀𝜑𝜒→→𝜑𝜓𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗𝜓] into ax-2
15748	→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓	Modus ponens 15746, 15747
15749	→→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓	Subs [𝜑↗→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
15750	→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓	Modus ponens 15748, 15749
15751	→→→𝜑𝜓→→⋀𝜑𝜒→𝜑𝜓→⋀𝜑𝜒𝜓→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜓] into ax-2
15752	→→→𝜑𝜓→⋀𝜑𝜒→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜓	Modus ponens 15750, 15751
15753	→→𝜑𝜓→⋀𝜑𝜒𝜓	Modus ponens 7486, 15752
15754	→⋀𝜑𝜒𝜒	Subs [𝜓↗𝜒] into simpr
15755	→𝜒→→𝜒𝜃𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜒𝜃] into ax-1
15756	→→𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒	Subs [𝜑↗→𝜒→→𝜒𝜃𝜒, 𝜓↗⋀𝜑𝜒] into ax-1
15757	→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒	Modus ponens 15755, 15756
15758	→→⋀𝜑𝜒→𝜒→→𝜒𝜃𝜒→→⋀𝜑𝜒𝜒→⋀𝜑𝜒→→𝜒𝜃𝜒	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗𝜒, 𝜒↗→→𝜒𝜃𝜒] into ax-2
15759	→→⋀𝜑𝜒𝜒→⋀𝜑𝜒→→𝜒𝜃𝜒	Modus ponens 15757, 15758
15760	→⋀𝜑𝜒→→𝜒𝜃𝜒	Modus ponens 15754, 15759
15761	→→→𝜒𝜃→𝜒𝜃→→→𝜒𝜃𝜒→→𝜒𝜃𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗𝜒, 𝜒↗𝜃] into ax-2
15762	→→→𝜒𝜃𝜒→→𝜒𝜃𝜃	Modus ponens 15736, 15761
15763	→→→→𝜒𝜃𝜒→→𝜒𝜃𝜃→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃	Subs [𝜑↗→→→𝜒𝜃𝜒→→𝜒𝜃𝜃, 𝜓↗⋀𝜑𝜒] into ax-1
15764	→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃	Modus ponens 15762, 15763
15765	→→⋀𝜑𝜒→→→𝜒𝜃𝜒→→𝜒𝜃𝜃→→⋀𝜑𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→→𝜒𝜃𝜃	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→→𝜒𝜃𝜒, 𝜒↗→→𝜒𝜃𝜃] into ax-2
15766	→→⋀𝜑𝜒→→𝜒𝜃𝜒→⋀𝜑𝜒→→𝜒𝜃𝜃	Modus ponens 15764, 15765
15767	→⋀𝜑𝜒→→𝜒𝜃𝜃	Modus ponens 15760, 15766
15768	→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗⋀𝜑𝜒] into ax-1
15769	→→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃	Subs [𝜑↗→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15770	→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃	Modus ponens 15768, 15769
15771	→→→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒→𝜒𝜃] into ax-2
15772	→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃	Modus ponens 15770, 15771
15773	→→⋀𝜑𝜒→→𝜒𝜃𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗⋀𝜑𝜒, 𝜓↗→𝜒𝜃, 𝜒↗𝜃] into ax-2
15774	→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15767, 15773
15775	→→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15776	→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15774, 15775
15777	→→→𝜒𝜃→→⋀𝜑𝜒→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→⋀𝜑𝜒→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
15778	→→→𝜒𝜃→⋀𝜑𝜒→𝜒𝜃→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15776, 15777
15779	→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15768, 15778
15780	→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀𝜑𝜒, 𝜒↗𝜃] into pm3.43
15781	↔⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into df-an
15782	→↔⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃] into bicom1
15783	↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Modus ponens 15781, 15782
15784	→↔¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃] into biimp
15785	→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Modus ponens 15783, 15784
15786	→→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15787	→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15780, 15786
15788	→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15789	→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃⋀→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15787, 15788
15790	→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15785, 15789
15791	→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into pm3.2im
15792	→→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15793	→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15790, 15792
15794	→→→⋀𝜑𝜒𝜃→¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15795	→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15793, 15794
15796	→→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜓] into ax-1
15797	→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15795, 15796
15798	→→→⋀𝜑𝜒𝜓→→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15799	→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃¬→→⋀𝜑𝜒𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15797, 15798
15800	→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15791, 15799
15801	→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃] into id
15802	→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜓] into ax-1
15803	→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15804	→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Modus ponens 15802, 15803
15805	→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃] into ax-2
15806	→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃	Modus ponens 15804, 15805
15807	→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15808	→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15800, 15807
15809	→→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15810	→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15808, 15809
15811	→→→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15812	→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15810, 15811
15813	→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15802, 15812
15814	→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓	Subs [𝜑↗→⋀𝜑𝜒𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15815	→→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓	Subs [𝜑↗→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
15816	→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓	Modus ponens 15814, 15815
15817	→→→𝜑𝜓→→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓] into ax-2
15818	→→→𝜑𝜓→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓	Modus ponens 15816, 15817
15819	→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓	Modus ponens 15753, 15818
15820	→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15821	→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15813, 15820
15822	→→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15823	→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15821, 15822
15824	→→→𝜑𝜓→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15825	→→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15823, 15824
15826	→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15819, 15825
15827	→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
15828	→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15829	→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15827, 15828
15830	→→→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15831	→→→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15829, 15830
15832	→→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15833	→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15826, 15832
15834	→→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15835	→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15833, 15834
15836	→→→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15837	→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15835, 15836
15838	→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15827, 15837
15839	→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
15840	→→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
15841	→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓	Modus ponens 15839, 15840
15842	→→→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→𝜑𝜓] into ax-2
15843	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓	Modus ponens 15841, 15842
15844	→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15845	→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15838, 15844
15846	→→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15847	→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15845, 15846
15848	→→→𝜑𝜓→→→⋀𝜑𝜒𝜃→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15849	→→→𝜑𝜓→→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15847, 15848
15850	↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into df-an
15851	→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃] into notnotr
15852	→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15853	→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15827, 15852
15854	→→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15855	→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15853, 15854
15856	→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15851, 15855
15857	→→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15858	→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15833, 15857
15859	→→¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15860	→→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15858, 15859
15861	→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15856, 15860
15862	→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15863	→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
15864	→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓	Modus ponens 15862, 15863
15865	→→→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓] into ax-2
15866	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓	Modus ponens 15864, 15865
15867	→→¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15868	→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15861, 15867
15869	→→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15870	→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15868, 15869
15871	→→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓, 𝜒↗→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15872	→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15870, 15871
15873	→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15862, 15872
15874	→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒⋀𝜓𝜃] into notnot
15875	→→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬→⋀𝜑𝜒𝜃] into ax-1
15876	→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15874, 15875
15877	→→¬¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒⋀𝜓𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬¬→⋀𝜑𝜒𝜃, 𝜓↗→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15878	→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15876, 15877
15879	→→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15880	→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15878, 15879
15881	→→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15882	→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15880, 15881
15883	→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15873, 15882
15884	→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-3
15885	→→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
15886	→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃	Modus ponens 15884, 15885
15887	→→→𝜑𝜓→→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃] into ax-2
15888	→→→𝜑𝜓→¬¬→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃	Modus ponens 15886, 15887
15889	→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃	Modus ponens 15883, 15888
15890	→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃] into id
15891	→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
15892	→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15893	→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15891, 15892
15894	→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15895	→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15893, 15894
15896	→→→𝜑𝜓→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬→⋀𝜑𝜒𝜃] into ax-2
15897	→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15889, 15896
15898	→→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15899	→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15897, 15898
15900	→→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15901	→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15899, 15900
15902	→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15891, 15901
15903	→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into id
15904	→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15905	→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15903, 15904
15906	→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into notnotr
15907	→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15908	→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15909	→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15907, 15908
15910	→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15911	→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15909, 15910
15912	→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15906, 15911
15913	→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15914	→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15905, 15913
15915	→→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15916	→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15914, 15915
15917	→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15918	→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15916, 15917
15919	→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
15920	→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15921	→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15919, 15920
15922	→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15923	→→¬→⋀𝜑𝜒⋀𝜓𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15921, 15922
15924	→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15925	→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15912, 15924
15926	→→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15927	→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15925, 15926
15928	→→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15929	→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒⋀𝜓𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15927, 15928
15930	→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15919, 15929
15931	→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-3
15932	→→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒⋀𝜓𝜃] into ax-1
15933	→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15931, 15932
15934	→→¬→⋀𝜑𝜒⋀𝜓𝜃→→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15935	→→¬→⋀𝜑𝜒⋀𝜓𝜃→¬¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15933, 15934
15936	→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15930, 15935
15937	→→¬→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
15938	→→¬→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15936, 15937
15939	→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15902, 15938
15940	→→¬→⋀𝜑𝜒⋀𝜓𝜃¬¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-3
15941	→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15939, 15940
15942	→↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into biimp
15943	→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 15850, 15942
15944	→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-1
15945	→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15941, 15944
15946	→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
15947	→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15945, 15946
15948	→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15943, 15947
15949	→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15950	→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15827, 15949
15951	→→→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15952	→→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15950, 15951
15953	→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15779, 15952
15954	↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into df-an
15955	→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜒𝜃→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
15956	→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Modus ponens 196, 15955
15957	→→¬¬→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜒𝜃→𝜑𝜓] into ax-2
15958	→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Modus ponens 15956, 15957
15959	→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓	Modus ponens 532, 15958
15960	→→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
15961	→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15953, 15960
15962	→→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1
15963	→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15961, 15962
15964	→→¬¬→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2
15965	→→¬¬→𝜑𝜓→→𝜒𝜃→𝜑𝜓→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15963, 15964
15966	→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15959, 15965
15967	→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1
15968	→→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃	Subs [𝜑↗→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15969	→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃	Modus ponens 15967, 15968
15970	→→→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓→𝜒𝜃] into ax-2
15971	→→→𝜒𝜃→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃	Modus ponens 15969, 15970
15972	→→¬¬→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
15973	→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15966, 15972
15974	→→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15975	→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15973, 15974
15976	→→→𝜒𝜃→→¬¬→𝜑𝜓→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓→𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
15977	→→→𝜒𝜃→¬¬→𝜑𝜓→𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15975, 15976
15978	→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15967, 15977
15979	→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃] into notnot
15980	→→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜑𝜓] into ax-1
15981	→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Modus ponens 15979, 15980
15982	→→¬¬→𝜑𝜓→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗¬¬→⋀𝜑𝜒𝜃] into ax-2
15983	→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃	Modus ponens 15981, 15982
15984	→→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15985	→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃	Modus ponens 15983, 15984
15986	→→→𝜒𝜃→→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃] into ax-2
15987	→→→𝜒𝜃→¬¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃	Modus ponens 15985, 15986
15988	→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃	Modus ponens 15978, 15987
15989	→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-3
15990	→→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓, 𝜓↗→𝜒𝜃] into ax-1
15991	→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓	Modus ponens 15989, 15990
15992	→→→𝜒𝜃→→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→𝜒𝜃, 𝜓↗→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓] into ax-2
15993	→→→𝜒𝜃→¬¬→𝜑𝜓¬¬→⋀𝜑𝜒𝜃→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓	Modus ponens 15991, 15992
15994	→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓	Modus ponens 15988, 15993
15995	→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃] into id
15996	→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
15997	→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
15998	→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃	Modus ponens 15996, 15997
15999	→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜒𝜃¬→⋀𝜑𝜒𝜃] into ax-2
16000	→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃	Modus ponens 15998, 15999
16001	→→→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→𝜑𝜓] into ax-2
16002	→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓	Modus ponens 15994, 16001
16003	→→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16004	→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16002, 16003
16005	→→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜒𝜃¬→𝜑𝜓] into ax-2
16006	→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16004, 16005
16007	→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓	Modus ponens 15996, 16006
16008	→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓] into id
16009	→→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16010	→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16008, 16009
16011	→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓] into notnotr
16012	→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16013	→→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16014	→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16012, 16013
16015	→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16016	→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16014, 16015
16017	→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16011, 16016
16018	→→¬→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16019	→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16010, 16018
16020	→→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16021	→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16019, 16020
16022	→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16023	→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16021, 16022
16024	→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16025	→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16026	→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 16024, 16025
16027	→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
16028	→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 16026, 16027
16029	→→¬¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→→𝜒𝜃¬→𝜑𝜓→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16030	→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16017, 16029
16031	→→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16032	→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16030, 16031
16033	→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16034	→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16032, 16033
16035	→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16024, 16034
16036	→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗→→𝜒𝜃¬→𝜑𝜓] into ax-3
16037	→→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16038	→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16036, 16037
16039	→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16040	→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜒𝜃¬→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16038, 16039
16041	→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16035, 16040
16042	→→¬→⋀𝜑𝜒𝜃→→→𝜒𝜃¬→𝜑𝜓¬¬→→𝜒𝜃¬→𝜑𝜓→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜒𝜃¬→𝜑𝜓, 𝜒↗¬¬→→𝜒𝜃¬→𝜑𝜓] into ax-2
16043	→→¬→⋀𝜑𝜒𝜃→→𝜒𝜃¬→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16041, 16042
16044	→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 16007, 16043
16045	→→¬→⋀𝜑𝜒𝜃¬¬→→𝜒𝜃¬→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-3
16046	→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16044, 16045
16047	→↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into biimp
16048	→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Modus ponens 15954, 16047
16049	→→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜒𝜃→𝜑𝜓] into ax-1
16050	→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16046, 16049
16051	→→⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16052	→→⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16050, 16051
16053	→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16048, 16052
16054	→↔⋀→𝜒𝜃→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓	Subs [𝜑↗⋀→𝜒𝜃→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into bicom1
16055	↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓	Modus ponens 15954, 16054
16056	→↔¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓	Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗⋀→𝜒𝜃→𝜑𝜓] into biimp
16057	→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓	Modus ponens 16055, 16056
16058	→→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓] into ax-1
16059	→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16053, 16058
16060	→→¬→→𝜒𝜃¬→𝜑𝜓→⋀→𝜒𝜃→𝜑𝜓→⋀𝜑𝜒𝜃→→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜓↗⋀→𝜒𝜃→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16061	→→¬→→𝜒𝜃¬→𝜑𝜓⋀→𝜒𝜃→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16059, 16060
16062	→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into pm3.2im
16063	→→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16064	→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16046, 16063
16065	→→→𝜑𝜓→¬→→𝜒𝜃¬→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16066	→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16064, 16065
16067	→→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗→𝜒𝜃] into ax-1
16068	→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16066, 16067
16069	→→→𝜒𝜃→→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜑𝜓→⋀𝜑𝜒𝜃→→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
16070	→→→𝜒𝜃→→𝜑𝜓¬→→𝜒𝜃¬→𝜑𝜓→→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16068, 16069
16071	→→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16072	→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 15961, 16071
16073	→→→𝜑𝜓→→→𝜒𝜃→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜒𝜃→𝜑𝜓, 𝜒↗→→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2
16074	→→→𝜑𝜓→→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16072, 16073
16075	→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 196, 16074
16076	↔⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into df-an
16077	→¬¬→𝜒𝜃→𝜒𝜃	Subs [𝜑↗→𝜒𝜃] into notnotr
16078	→→𝜒𝜃→→𝜑𝜓→𝜒𝜃	Subs [𝜑↗→𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16079	→→→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃	Subs [𝜑↗→→𝜒𝜃→→𝜑𝜓→𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1
16080	→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃	Modus ponens 16078, 16079
16081	→→¬¬→𝜒𝜃→→𝜒𝜃→→𝜑𝜓→𝜒𝜃→→¬¬→𝜒𝜃→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃	Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→𝜒𝜃, 𝜒↗→→𝜑𝜓→𝜒𝜃] into ax-2
16082	→→¬¬→𝜒𝜃→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃	Modus ponens 16080, 16081
16083	→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃	Modus ponens 16077, 16082
16084	→→→𝜑𝜓→→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16085	→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16075, 16084
16086	→→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1
16087	→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16085, 16086
16088	→→¬¬→𝜒𝜃→→→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→→𝜑𝜓→𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
16089	→→¬¬→𝜒𝜃→→𝜑𝜓→𝜒𝜃→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16087, 16088
16090	→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16083, 16089
16091	→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬→𝜒𝜃] into ax-1
16092	→→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
16093	→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓	Modus ponens 16091, 16092
16094	→→→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬→𝜒𝜃→𝜑𝜓] into ax-2
16095	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓	Modus ponens 16093, 16094
16096	→→¬¬→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16097	→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16090, 16096
16098	→→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16099	→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16097, 16098
16100	→→→𝜑𝜓→→¬¬→𝜒𝜃→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃→𝜑𝜓, 𝜒↗→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃] into ax-2
16101	→→→𝜑𝜓→¬¬→𝜒𝜃→𝜑𝜓→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16099, 16100
16102	→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16091, 16101
16103	→→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬→𝜒𝜃] into ax-1
16104	→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Modus ponens 15979, 16103
16105	→→¬¬→𝜒𝜃→→⋀𝜑𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬¬→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗¬¬→⋀𝜑𝜒𝜃] into ax-2
16106	→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Modus ponens 16104, 16105
16107	→→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16108	→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Modus ponens 16106, 16107
16109	→→→𝜑𝜓→→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜒↗→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃] into ax-2
16110	→→→𝜑𝜓→¬¬→𝜒𝜃→⋀𝜑𝜒𝜃→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Modus ponens 16108, 16109
16111	→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃	Modus ponens 16102, 16110
16112	→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃	Subs [𝜑↗¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-3
16113	→→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃	Subs [𝜑↗→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16114	→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃	Modus ponens 16112, 16113
16115	→→→𝜑𝜓→→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃] into ax-2
16116	→→→𝜑𝜓→¬¬→𝜒𝜃¬¬→⋀𝜑𝜒𝜃→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃	Modus ponens 16114, 16115
16117	→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃	Modus ponens 16111, 16116
16118	→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→𝜑𝜓] into ax-1
16119	→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16120	→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 16118, 16119
16121	→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-2
16122	→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Modus ponens 16120, 16121
16123	→→→𝜑𝜓→¬→⋀𝜑𝜒𝜃¬→𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→𝜒𝜃] into ax-2
16124	→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16117, 16123
16125	→→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16126	→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16124, 16125
16127	→→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓¬→𝜒𝜃] into ax-2
16128	→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16126, 16127
16129	→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16118, 16128
16130	→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃] into id
16131	→→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16132	→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16130, 16131
16133	→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃] into notnotr
16134	→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16135	→→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1
16136	→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16134, 16135
16137	→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16138	→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16136, 16137
16139	→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16133, 16138
16140	→→¬→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16141	→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16132, 16140
16142	→→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1
16143	→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16141, 16142
16144	→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16145	→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16143, 16144
16146	→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-1
16147	→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16148	→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃	Modus ponens 16146, 16147
16149	→→¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃] into ax-2
16150	→→¬→⋀𝜑𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃	Modus ponens 16148, 16149
16151	→→¬¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃, 𝜒↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16152	→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16139, 16151
16153	→→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16154	→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16152, 16153
16155	→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃, 𝜒↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16156	→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→⋀𝜑𝜒𝜃→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16154, 16155
16157	→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16146, 16156
16158	→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗→→𝜑𝜓¬→𝜒𝜃] into ax-3
16159	→→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃, 𝜓↗¬→⋀𝜑𝜒𝜃] into ax-1
16160	→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16158, 16159
16161	→→¬→⋀𝜑𝜒𝜃→→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16162	→→¬→⋀𝜑𝜒𝜃→¬¬¬→→𝜑𝜓¬→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16160, 16161
16163	→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16157, 16162
16164	→→¬→⋀𝜑𝜒𝜃→→→𝜑𝜓¬→𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗¬→⋀𝜑𝜒𝜃, 𝜓↗→→𝜑𝜓¬→𝜒𝜃, 𝜒↗¬¬→→𝜑𝜓¬→𝜒𝜃] into ax-2
16165	→→¬→⋀𝜑𝜒𝜃→→𝜑𝜓¬→𝜒𝜃→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16163, 16164
16166	→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16129, 16165
16167	→→¬→⋀𝜑𝜒𝜃¬¬→→𝜑𝜓¬→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃] into ax-3
16168	→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16166, 16167
16169	→↔⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃] into biimp
16170	→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃	Modus ponens 16076, 16169
16171	→→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16172	→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16168, 16171
16173	→→⋀→𝜑𝜓→𝜒𝜃→¬→→𝜑𝜓¬→𝜒𝜃→⋀𝜑𝜒𝜃→→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→𝜒𝜃, 𝜒↗→⋀𝜑𝜒𝜃] into ax-2
16174	→→⋀→𝜑𝜓→𝜒𝜃¬→→𝜑𝜓¬→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16172, 16173
16175	→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃	Modus ponens 16170, 16174
16176	→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒𝜃] into simpl
16177	→↔⋀→𝜑𝜓→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into bicom1
16178	↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15850, 16177
16179	→↔¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃] into biimp
16180	→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16178, 16179
16181	→→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃] into ax-1
16182	→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15948, 16181
16183	→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16184	→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃⋀→𝜑𝜓→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16182, 16183
16185	→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀𝜑𝜒𝜃] into pm3.2im
16186	→→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→⋀𝜑𝜒𝜃] into ax-1
16187	→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15941, 16186
16188	→→→⋀𝜑𝜒𝜃→¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→⋀𝜑𝜒𝜃, 𝜓↗¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16189	→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16187, 16188
16190	→→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
16191	→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16189, 16190
16192	→→→𝜑𝜓→→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃, 𝜒↗→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16193	→→→𝜑𝜓→→⋀𝜑𝜒𝜃¬→→𝜑𝜓¬→⋀𝜑𝜒𝜃→→𝜑𝜓→→⋀𝜑𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16191, 16192
16194	→→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16195	→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 15827, 16194
16196	→→⋀→𝜑𝜓→𝜒𝜃→→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒𝜃] into ax-2
16197	→→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16195, 16196
16198	→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃	Modus ponens 16175, 16197
16199	→→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16200	→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 15833, 16199
16201	→→⋀→𝜑𝜓→𝜒𝜃→→→𝜑𝜓→⋀𝜑𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→→𝜑𝜓→⋀𝜑𝜒𝜃, 𝜒↗→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16202	→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16200, 16201
16203	→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16198, 16202
16204	→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16205	→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
16206	→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓	Modus ponens 16204, 16205
16207	→→→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓] into ax-2
16208	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓	Modus ponens 16206, 16207
16209	→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16210	→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16203, 16209
16211	→→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗→𝜑𝜓] into ax-1
16212	→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16210, 16211
16213	→→→𝜑𝜓→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→𝜑𝜓, 𝜓↗→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16214	→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16212, 16213
16215	→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16204, 16214
16216	→→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃] into ax-1
16217	→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16215, 16216
16218	→→⋀→𝜑𝜓→𝜒𝜃→→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗→𝜑𝜓, 𝜒↗→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16219	→→⋀→𝜑𝜓→𝜒𝜃→𝜑𝜓→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16217, 16218
16220	→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16176, 16219
16221	→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃] into id
16222	→→⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃→→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Subs [𝜑↗⋀→𝜑𝜓→𝜒𝜃, 𝜓↗⋀→𝜑𝜓→𝜒𝜃, 𝜒↗→⋀𝜑𝜒⋀𝜓𝜃] into ax-2
16223	→→⋀→𝜑𝜓→𝜒𝜃⋀→𝜑𝜓→𝜒𝜃→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16220, 16222
16224	→⋀→𝜑𝜓→𝜒𝜃→⋀𝜑𝜒⋀𝜓𝜃	Modus ponens 16221, 16223	anim12
16225	→→𝜓→𝜑𝜓→⋀𝜑𝜓→𝜓→𝜑𝜓	Subs [𝜑↗→𝜓→𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
16226	→⋀𝜑𝜓→𝜓→𝜑𝜓	Modus ponens 208, 16225
16227	→→⋀𝜑𝜓→𝜓→𝜑𝜓→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
16228	→→⋀𝜑𝜓𝜓→⋀𝜑𝜓→𝜑𝜓	Modus ponens 16226, 16227
16229	→⋀𝜑𝜓→𝜑𝜓	Modus ponens simpr, 16228	pm3.4
16230	↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑	Subs [𝜓↗⋀𝜓𝜑] into bicom
16231	↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜓↗⋀𝜓𝜒] into bicom
16232	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into id
16233	→↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16234	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 7683, 16233
16235	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74
16236	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp
16237	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Modus ponens 16235, 16236
16238	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Modus ponens 16232, 16237
16239	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74
16240	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16241	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16239, 16240
16242	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16234, 16241
16243	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16244	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16242, 16243
16245	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp
16246	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Modus ponens 16238, 16245
16247	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16248	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16244, 16247
16249	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16250	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16248, 16249
16251	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16246, 16250
16252	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16253	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Modus ponens 16242, 16252
16254	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into biimp
16255	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒	Modus ponens 16253, 16254
16256	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒] into bicom1
16257	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16238, 16256
16258	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16259	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16257, 16258
16260	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16261	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16259, 16260
16262	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16263	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16261, 16262
16264	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16255, 16263
16265	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16266	→→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16251, 16265
16267	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16264, 16266
16268	↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74
16269	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16270	↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16268, 16269
16271	→↔↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16272	→↔→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16270, 16271
16273	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16267, 16272
16274	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into id
16275	→↔→𝜓↔𝜑𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16276	↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 7683, 16275
16277	→↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16278	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16276, 16277
16279	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑⋀𝜓𝜒] into pm5.74
16280	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16281	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16279, 16280
16282	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16274, 16281
16283	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74
16284	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16285	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16283, 16284
16286	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16278, 16285
16287	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16288	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16286, 16287
16289	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16290	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16282, 16289
16291	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1
16292	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16288, 16291
16293	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2
16294	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16292, 16293
16295	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16290, 16294
16296	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1
16297	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16286, 16296
16298	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16299	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16297, 16298
16300	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16301	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16282, 16300
16302	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16303	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16301, 16302
16304	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16305	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16303, 16304
16306	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-2
16307	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16305, 16306
16308	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16299, 16307
16309	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into impbi
16310	→→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16295, 16309
16311	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16308, 16310
16312	↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗→𝜓↔𝜑𝜒] into pm5.74
16313	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1
16314	↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16312, 16313
16315	→↔↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16316	→↔→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16314, 16315
16317	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16311, 16316
16318	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16319	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16273, 16318
16320	↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16317, 16319
16321	↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒] into bicom
16322	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into id
16323	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1
16324	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16231, 16323
16325	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74
16326	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16327	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16325, 16326
16328	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16322, 16327
16329	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74
16330	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16331	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16329, 16330
16332	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16324, 16331
16333	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16334	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16332, 16333
16335	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16336	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16328, 16335
16337	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16338	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16334, 16337
16339	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-2
16340	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16338, 16339
16341	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16336, 16340
16342	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1
16343	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16332, 16342
16344	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16345	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16343, 16344
16346	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into bicom1
16347	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16328, 16346
16348	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16349	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16347, 16348
16350	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-1
16351	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16349, 16350
16352	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16353	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16351, 16352
16354	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16345, 16353
16355	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into impbi
16356	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16341, 16355
16357	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16354, 16356
16358	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74
16359	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1
16360	↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16358, 16359
16361	→↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16362	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16360, 16361
16363	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16357, 16362
16364	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into id
16365	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜒𝜑] into bicom1
16366	↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16231, 16365
16367	→↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into ax-1
16368	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16366, 16367
16369	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜒𝜑] into pm5.74
16370	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp
16371	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Modus ponens 16369, 16370
16372	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Modus ponens 16364, 16371
16373	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜒𝜑, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74
16374	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into biimp
16375	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16373, 16374
16376	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16368, 16375
16377	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into biimp
16378	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16376, 16377
16379	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp
16380	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Modus ponens 16372, 16379
16381	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16382	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16378, 16381
16383	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into ax-2
16384	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16382, 16383
16385	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16380, 16384
16386	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into bicom1
16387	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Modus ponens 16376, 16386
16388	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into biimp
16389	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑	Modus ponens 16387, 16388
16390	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑] into bicom1
16391	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16372, 16390
16392	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16393	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16391, 16392
16394	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into ax-1
16395	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16393, 16394
16396	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑, 𝜒↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16397	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16395, 16396
16398	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16389, 16397
16399	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into impbi
16400	→→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16385, 16399
16401	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Modus ponens 16398, 16400
16402	↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔𝜑⋀𝜓𝜒] into pm5.74
16403	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒] into bicom1
16404	↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16402, 16403
16405	→↔↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒, 𝜓↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16406	→↔→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16404, 16405
16407	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16401, 16406
16408	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into impbi
16409	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16363, 16408
16410	↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16407, 16409
16411	↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜒𝜑] into bicom
16412	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16413	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16411, 16412
16414	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16415	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-1
16416	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16413, 16415
16417	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16418	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16416, 16417
16419	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16363, 16418
16420	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16421	↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16411, 16420
16422	→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into biimp
16423	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑	Modus ponens 16421, 16422
16424	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑] into bicom1
16425	↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16410, 16424
16426	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16427	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16428	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16407, 16427
16429	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑, 𝜒↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into ax-2
16430	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜒𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16428, 16429
16431	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16423, 16430
16432	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16433	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16419, 16432
16434	↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16431, 16433
16435	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16436	→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16437	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16321, 16436
16438	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16439	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16419, 16438
16440	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16441	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16439, 16440
16442	→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16437, 16441
16443	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16444	↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16434, 16443
16445	→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into biimp
16446	→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒] into bicom1
16447	↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16321, 16446
16448	→↔↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16449	→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16447, 16448
16450	→→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16451	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16449, 16450
16452	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16453	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16451, 16452
16454	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16431, 16453
16455	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16456	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16442, 16455
16457	↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16454, 16456
16458	→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16459	→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16460	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16461	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16442, 16460
16462	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-2
16463	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16461, 16462
16464	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16273, 16463
16465	→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16466	↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16457, 16465
16467	→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16468	→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16469	↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16320, 16468
16470	→↔↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16471	→→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into ax-1
16472	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16317, 16471
16473	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2
16474	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑⋀𝜓𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16472, 16473
16475	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16454, 16474
16476	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into impbi
16477	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16464, 16476
16478	↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16475, 16477
16479	↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→𝜓↔𝜑𝜒, 𝜓↗↔𝜑⋀𝜓𝜒] into bicom
16480	↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜑, 𝜓↗𝜑, 𝜒↗⋀𝜓𝜒] into biluk
16481	→↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16482	↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16480, 16481
16483	→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16484	→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16482, 16483
16485	→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16486	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-1
16487	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16484, 16486
16488	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔⋀𝜓𝜑𝜑] into ax-2
16489	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16487, 16488
16490	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16464, 16489
16491	→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16492	→↔↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into biimp
16493	→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒	Modus ponens 16480, 16492
16494	→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒] into bicom1
16495	↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16478, 16494
16496	→↔↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16497	→→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into ax-1
16498	→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16475, 16497
16499	→→↔⋀𝜓𝜑𝜑→↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒, 𝜒↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into ax-2
16500	→→↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜒𝜑↔⋀𝜓𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16498, 16499
16501	→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16493, 16500
16502	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into impbi
16503	→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16490, 16502
16504	↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16501, 16503
16505	→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16506	→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16507	→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16479, 16506
16508	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16509	→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16490, 16508
16510	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜒↗↔⋀𝜓𝜑𝜑] into ax-2
16511	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16509, 16510
16512	→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16507, 16511
16513	→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16514	↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Modus ponens 16504, 16513
16515	→↔↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into biimp
16516	→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒] into bicom1
16517	↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16479, 16516
16518	→↔↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16519	→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16517, 16518
16520	→→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into ax-1
16521	→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16519, 16520
16522	→→↔⋀𝜓𝜑𝜑→↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16523	→→↔⋀𝜓𝜑𝜑↔↔𝜑⋀𝜓𝜒→𝜓↔𝜑𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16521, 16522
16524	→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16501, 16523
16525	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into impbi
16526	→→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16512, 16525
16527	↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Modus ponens 16524, 16526
16528	→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16529	↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16527, 16528
16530	→↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16531	→↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16532	→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑	Modus ponens 16230, 16531
16533	→→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑] into ax-1
16534	→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16524, 16533
16535	→→↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16536	→→↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16534, 16535
16537	→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16532, 16536
16538	→↔↔⋀𝜓𝜑𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into bicom1
16539	→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑] into biimp
16540	→↔↔𝜑⋀𝜓𝜑↔⋀𝜓𝜑𝜑↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔⋀𝜓𝜑𝜑] into bicom1
16541	↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑	Modus ponens 16230, 16540
16542	→↔↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔⋀𝜓𝜑𝜑, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
16543	→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑	Modus ponens 16541, 16542
16544	→→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑	Subs [𝜑↗→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16545	→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑	Modus ponens 16543, 16544
16546	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔⋀𝜓𝜑𝜑↔𝜑⋀𝜓𝜑→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔⋀𝜓𝜑𝜑, 𝜒↗↔𝜑⋀𝜓𝜑] into ax-2
16547	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔⋀𝜓𝜑𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑	Modus ponens 16545, 16546
16548	→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑	Modus ponens 16512, 16547
16549	→→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into impbi
16550	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16537, 16549
16551	↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16548, 16550
16552	→↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into biimp
16553	→↔→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔𝜑⋀𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
16554	→→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗→𝜑𝜓] into ax-1
16555	→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16537, 16554
16556	→→→𝜑𝜓→↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑, 𝜒↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-2
16557	→→→𝜑𝜓↔𝜑⋀𝜓𝜑→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16555, 16556
16558	→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 6441, 16557
16559	→↔↔𝜑⋀𝜓𝜑↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into bicom1
16560	↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑	Modus ponens 16551, 16559
16561	→↔↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑] into biimp
16562	→↔→𝜑𝜓↔𝜑⋀𝜓𝜑↔↔𝜑⋀𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔𝜑⋀𝜓𝜑] into bicom1
16563	↔↔𝜑⋀𝜓𝜑→𝜑𝜓	Modus ponens pm4.71r, 16562
16564	→↔↔𝜑⋀𝜓𝜑→𝜑𝜓→↔𝜑⋀𝜓𝜑→𝜑𝜓	Subs [𝜑↗↔𝜑⋀𝜓𝜑, 𝜓↗→𝜑𝜓] into biimp
16565	→→↔𝜑⋀𝜓𝜑→𝜑𝜓→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓	Subs [𝜑↗→↔𝜑⋀𝜓𝜑→𝜑𝜓, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into ax-1
16566	→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓	Modus ponens 6452, 16565
16567	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→↔𝜑⋀𝜓𝜑→𝜑𝜓→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓	Subs [𝜑↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒, 𝜓↗↔𝜑⋀𝜓𝜑, 𝜒↗→𝜑𝜓] into ax-2
16568	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒↔𝜑⋀𝜓𝜑→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 16566, 16567
16569	→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓	Modus ponens 16548, 16568
16570	→→→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒] into impbi
16571	→→↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒→𝜑𝜓↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16558, 16570
16572	↔→𝜑𝜓↔→𝜓↔𝜑𝜒↔𝜑⋀𝜓𝜒	Modus ponens 16569, 16571	biadan
16573	→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into biimp
16574	→→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓	Subs [𝜑↗→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16575	→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓	Modus ponens 16573, 16574
16576	→→𝜑→↔𝜓↔𝜑𝜓→𝜓↔𝜑𝜓→→𝜑↔𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓	Subs [𝜓↗↔𝜓↔𝜑𝜓, 𝜒↗→𝜓↔𝜑𝜓] into ax-2
16577	→→𝜑↔𝜓↔𝜑𝜓→𝜑→𝜓↔𝜑𝜓	Modus ponens 16575, 16576
16578	→→𝜑→𝜓↔𝜑𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜒↗↔𝜑𝜓] into ax-2
16579	→→→𝜑𝜓→𝜑↔𝜑𝜓→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
16580	→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓	Modus ponens 1697, 16579
16581	→→¬¬𝜓→→𝜑𝜓→𝜑↔𝜑𝜓→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑↔𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑↔𝜑𝜓] into ax-2
16582	→→¬¬𝜓→𝜑𝜓→¬¬𝜓→𝜑↔𝜑𝜓	Modus ponens 16580, 16581
16583	→¬¬𝜓→𝜑↔𝜑𝜓	Modus ponens 575, 16582
16584	→→¬¬𝜓→𝜑↔𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16585	→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓	Modus ponens 16583, 16584
16586	→→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16587	→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓	Modus ponens 16585, 16586
16588	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓↔𝜑𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓↔𝜑𝜓	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓↔𝜑𝜓] into ax-2
16589	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓↔𝜑𝜓	Modus ponens 16587, 16588
16590	→𝜑→¬¬𝜓↔𝜑𝜓	Modus ponens 581, 16589
16591	→↔𝜑𝜓¬¬↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓] into notnot
16592	→→↔𝜑𝜓¬¬↔𝜑𝜓→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
16593	→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓	Modus ponens 16591, 16592
16594	→→¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2
16595	→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16593, 16594
16596	→→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓	Subs [𝜑↗→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16597	→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16595, 16596
16598	→→𝜑→→¬¬𝜓↔𝜑𝜓→¬¬𝜓¬¬↔𝜑𝜓→→𝜑→¬¬𝜓↔𝜑𝜓→𝜑→¬¬𝜓¬¬↔𝜑𝜓	Subs [𝜓↗→¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬𝜓¬¬↔𝜑𝜓] into ax-2
16599	→→𝜑→¬¬𝜓↔𝜑𝜓→𝜑→¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16597, 16598
16600	→𝜑→¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16590, 16599
16601	→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-3
16602	→→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
16603	→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓	Modus ponens 16601, 16602
16604	→→𝜑→→¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬𝜓→→𝜑→¬¬𝜓¬¬↔𝜑𝜓→𝜑→¬↔𝜑𝜓¬𝜓	Subs [𝜓↗→¬¬𝜓¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬𝜓] into ax-2
16605	→→𝜑→¬¬𝜓¬¬↔𝜑𝜓→𝜑→¬↔𝜑𝜓¬𝜓	Modus ponens 16603, 16604
16606	→𝜑→¬↔𝜑𝜓¬𝜓	Modus ponens 16600, 16605
16607	→¬↔𝜑𝜓¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓] into id
16608	→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗𝜑] into ax-1
16609	→→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓	Subs [𝜑↗→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16610	→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓	Modus ponens 16608, 16609
16611	→→¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→𝜑¬↔𝜑𝜓] into ax-2
16612	→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓	Modus ponens 16610, 16611
16613	→→𝜑→¬↔𝜑𝜓¬𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓	Subs [𝜓↗¬↔𝜑𝜓, 𝜒↗¬𝜓] into ax-2
16614	→→𝜑¬↔𝜑𝜓→𝜑¬𝜓	Modus ponens 16606, 16613
16615	→→→𝜑¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓	Subs [𝜑↗→→𝜑¬↔𝜑𝜓→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16616	→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓	Modus ponens 16614, 16615
16617	→→¬↔𝜑𝜓→→𝜑¬↔𝜑𝜓→𝜑¬𝜓→→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜑¬↔𝜑𝜓, 𝜒↗→𝜑¬𝜓] into ax-2
16618	→→¬↔𝜑𝜓→𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→𝜑¬𝜓	Modus ponens 16616, 16617
16619	→¬↔𝜑𝜓→𝜑¬𝜓	Modus ponens 16608, 16618
16620	→→¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16621	→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 619, 16620
16622	→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16623	→→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
16624	→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Modus ponens 16622, 16623
16625	→→¬¬¬→𝜑¬𝜓→¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→𝜑¬𝜓] into ax-2
16626	→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Modus ponens 16624, 16625
16627	→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Modus ponens 622, 16626
16628	→→¬↔𝜑𝜓→¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
16629	→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Modus ponens 16621, 16628
16630	→→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
16631	→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Modus ponens 16629, 16630
16632	→→¬¬¬→𝜑¬𝜓→→¬↔𝜑𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗→¬↔𝜑𝜓¬→𝜑¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→𝜑¬𝜓] into ax-2
16633	→→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓	Modus ponens 16631, 16632
16634	→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬¬→𝜑¬𝜓] into ax-1
16635	→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16636	→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 16634, 16635
16637	→→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓] into ax-2
16638	→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓	Modus ponens 16636, 16637
16639	→→¬¬¬→𝜑¬𝜓→¬↔𝜑𝜓¬→𝜑¬𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬¬¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬→𝜑¬𝜓] into ax-2
16640	→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 16627, 16639
16641	→→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16642	→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 16640, 16641
16643	→→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓, 𝜒↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓] into ax-2
16644	→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 16642, 16643
16645	→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓	Modus ponens 16634, 16644
16646	→→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16647	→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 647, 16646
16648	→→¬↔𝜑𝜓→→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓, 𝜒↗→→𝜑¬𝜓¬¬→𝜑¬𝜓] into ax-2
16649	→→¬↔𝜑𝜓→¬¬¬→𝜑¬𝜓¬→𝜑¬𝜓→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 16647, 16648
16650	→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓	Modus ponens 16645, 16649
16651	→→¬↔𝜑𝜓→→𝜑¬𝜓¬¬→𝜑¬𝜓→→¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓¬¬→𝜑¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜑¬𝜓, 𝜒↗¬¬→𝜑¬𝜓] into ax-2
16652	→→¬↔𝜑𝜓→𝜑¬𝜓→¬↔𝜑𝜓¬¬→𝜑¬𝜓	Modus ponens 16650, 16651
16653	→¬↔𝜑𝜓¬¬→𝜑¬𝜓	Modus ponens 16619, 16652
16654	→→¬↔𝜑𝜓¬¬→𝜑¬𝜓→¬→𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→𝜑¬𝜓] into ax-3
16655	→¬→𝜑¬𝜓↔𝜑𝜓	Modus ponens 16653, 16654
16656	→→¬→𝜑¬𝜓↔𝜑𝜓→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬→𝜑¬𝜓↔𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
16657	→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓	Modus ponens 16655, 16656
16658	→→⋀𝜑𝜓→¬→𝜑¬𝜓↔𝜑𝜓→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓↔𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬→𝜑¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16659	→→⋀𝜑𝜓¬→𝜑¬𝜓→⋀𝜑𝜓↔𝜑𝜓	Modus ponens 16657, 16658
16660	→⋀𝜑𝜓↔𝜑𝜓	Modus ponens 4842, 16659	pm5.1
16661	↔⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓] into df-an
16662	→¬¬¬𝜓¬𝜓	Subs [𝜑↗¬𝜓] into notnotr
16663	→¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬𝜑] into ax-1
16664	→→¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗→¬𝜓→¬𝜑¬𝜓, 𝜓↗¬¬¬𝜓] into ax-1
16665	→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓	Modus ponens 16663, 16664
16666	→→¬¬¬𝜓→¬𝜓→¬𝜑¬𝜓→→¬¬¬𝜓¬𝜓→¬¬¬𝜓→¬𝜑¬𝜓	Subs [𝜑↗¬¬¬𝜓, 𝜓↗¬𝜓, 𝜒↗→¬𝜑¬𝜓] into ax-2
16667	→→¬¬¬𝜓¬𝜓→¬¬¬𝜓→¬𝜑¬𝜓	Modus ponens 16665, 16666
16668	→¬¬¬𝜓→¬𝜑¬𝜓	Modus ponens 16662, 16667
16669	→→¬𝜑→¬𝜓↔𝜑𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16670	→→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓, 𝜓↗¬¬¬𝜓] into ax-1
16671	→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 3133, 16670
16672	→→¬¬¬𝜓→→¬𝜑¬𝜓→¬𝜑↔𝜑𝜓→→¬¬¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜑↔𝜑𝜓	Subs [𝜑↗¬¬¬𝜓, 𝜓↗→¬𝜑¬𝜓, 𝜒↗→¬𝜑↔𝜑𝜓] into ax-2
16673	→→¬¬¬𝜓→¬𝜑¬𝜓→¬¬¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 16671, 16672
16674	→¬¬¬𝜓→¬𝜑↔𝜑𝜓	Modus ponens 16668, 16673
16675	→¬𝜑→¬¬¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬¬¬𝜓] into ax-1
16676	→→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑	Subs [𝜑↗→¬𝜑→¬¬¬𝜓¬𝜑, 𝜓↗¬𝜑] into ax-1
16677	→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑	Modus ponens 16675, 16676
16678	→→¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑→→¬𝜑¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑	Subs [𝜑↗¬𝜑, 𝜓↗¬𝜑, 𝜒↗→¬¬¬𝜓¬𝜑] into ax-2
16679	→→¬𝜑¬𝜑→¬𝜑→¬¬¬𝜓¬𝜑	Modus ponens 16677, 16678
16680	→→¬¬¬𝜓→¬𝜑↔𝜑𝜓→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓	Subs [𝜑↗¬¬¬𝜓, 𝜓↗¬𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16681	→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓	Modus ponens 16674, 16680
16682	→→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓	Subs [𝜑↗→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
16683	→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓	Modus ponens 16681, 16682
16684	→→¬𝜑→→¬¬¬𝜓¬𝜑→¬¬¬𝜓↔𝜑𝜓→→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬¬¬𝜓↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓¬𝜑, 𝜒↗→¬¬¬𝜓↔𝜑𝜓] into ax-2
16685	→→¬𝜑→¬¬¬𝜓¬𝜑→¬𝜑→¬¬¬𝜓↔𝜑𝜓	Modus ponens 16683, 16684
16686	→¬𝜑→¬¬¬𝜓↔𝜑𝜓	Modus ponens 16675, 16685
16687	→→↔𝜑𝜓¬¬↔𝜑𝜓→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬¬¬𝜓] into ax-1
16688	→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓	Modus ponens 16591, 16687
16689	→→¬¬¬𝜓→↔𝜑𝜓¬¬↔𝜑𝜓→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓	Subs [𝜑↗¬¬¬𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2
16690	→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16688, 16689
16691	→→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓	Subs [𝜑↗→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
16692	→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16690, 16691
16693	→→¬𝜑→→¬¬¬𝜓↔𝜑𝜓→¬¬¬𝜓¬¬↔𝜑𝜓→→¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓↔𝜑𝜓, 𝜒↗→¬¬¬𝜓¬¬↔𝜑𝜓] into ax-2
16694	→→¬𝜑→¬¬¬𝜓↔𝜑𝜓→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16692, 16693
16695	→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓	Modus ponens 16686, 16694
16696	→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-3
16697	→→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓	Subs [𝜑↗→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓, 𝜓↗¬𝜑] into ax-1
16698	→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓	Modus ponens 16696, 16697
16699	→→¬𝜑→→¬¬¬𝜓¬¬↔𝜑𝜓→¬↔𝜑𝜓¬¬𝜓→→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→¬↔𝜑𝜓¬¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗→¬¬¬𝜓¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬¬𝜓] into ax-2
16700	→→¬𝜑→¬¬¬𝜓¬¬↔𝜑𝜓→¬𝜑→¬↔𝜑𝜓¬¬𝜓	Modus ponens 16698, 16699
16701	→¬𝜑→¬↔𝜑𝜓¬¬𝜓	Modus ponens 16695, 16700
16702	→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬𝜑] into ax-1
16703	→→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓	Subs [𝜑↗→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16704	→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓	Modus ponens 16702, 16703
16705	→→¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬𝜑¬↔𝜑𝜓] into ax-2
16706	→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓	Modus ponens 16704, 16705
16707	→→¬𝜑→¬↔𝜑𝜓¬¬𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓	Subs [𝜑↗¬𝜑, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬¬𝜓] into ax-2
16708	→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓	Modus ponens 16701, 16707
16709	→→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓	Subs [𝜑↗→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16710	→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓	Modus ponens 16708, 16709
16711	→→¬↔𝜑𝜓→→¬𝜑¬↔𝜑𝜓→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬𝜑¬↔𝜑𝜓, 𝜒↗→¬𝜑¬¬𝜓] into ax-2
16712	→→¬↔𝜑𝜓→¬𝜑¬↔𝜑𝜓→¬↔𝜑𝜓→¬𝜑¬¬𝜓	Modus ponens 16710, 16711
16713	→¬↔𝜑𝜓→¬𝜑¬¬𝜓	Modus ponens 16702, 16712
16714	→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬→¬𝜑¬¬𝜓] into id
16715	→→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16716	→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16714, 16715
16717	→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬→¬𝜑¬¬𝜓] into notnotr
16718	→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16719	→→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1
16720	→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16718, 16719
16721	→→¬¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓] into ax-2
16722	→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16720, 16721
16723	→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16717, 16722
16724	→→¬↔𝜑𝜓→¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗¬→¬𝜑¬¬𝜓] into ax-2
16725	→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16716, 16724
16726	→→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1
16727	→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16725, 16726
16728	→→¬¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓, 𝜒↗→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓] into ax-2
16729	→→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16727, 16728
16730	→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬¬¬→¬𝜑¬¬𝜓] into ax-1
16731	→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓	Subs [𝜑↗→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16732	→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓	Modus ponens 16730, 16731
16733	→→¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓] into ax-2
16734	→→¬↔𝜑𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓	Modus ponens 16732, 16733
16735	→→¬¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬→¬𝜑¬¬𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬¬¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓, 𝜒↗¬→¬𝜑¬¬𝜓] into ax-2
16736	→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16723, 16735
16737	→→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16738	→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16736, 16737
16739	→→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓, 𝜒↗→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓] into ax-2
16740	→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬↔𝜑𝜓→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16738, 16739
16741	→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16730, 16740
16742	→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬¬→¬𝜑¬¬𝜓, 𝜓↗→¬𝜑¬¬𝜓] into ax-3
16743	→→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓	Subs [𝜑↗→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16744	→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓	Modus ponens 16742, 16743
16745	→→¬↔𝜑𝜓→→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓, 𝜒↗→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓] into ax-2
16746	→→¬↔𝜑𝜓→¬¬¬→¬𝜑¬¬𝜓¬→¬𝜑¬¬𝜓→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓	Modus ponens 16744, 16745
16747	→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓	Modus ponens 16741, 16746
16748	→→¬↔𝜑𝜓→→¬𝜑¬¬𝜓¬¬→¬𝜑¬¬𝜓→→¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→¬𝜑¬¬𝜓, 𝜒↗¬¬→¬𝜑¬¬𝜓] into ax-2
16749	→→¬↔𝜑𝜓→¬𝜑¬¬𝜓→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓	Modus ponens 16747, 16748
16750	→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓	Modus ponens 16713, 16749
16751	→→¬↔𝜑𝜓¬¬→¬𝜑¬¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→¬𝜑¬¬𝜓] into ax-3
16752	→¬→¬𝜑¬¬𝜓↔𝜑𝜓	Modus ponens 16750, 16751
16753	→↔⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓	Subs [𝜑↗⋀¬𝜑¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓] into biimp
16754	→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓	Modus ponens 16661, 16753
16755	→→¬→¬𝜑¬¬𝜓↔𝜑𝜓→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓	Subs [𝜑↗→¬→¬𝜑¬¬𝜓↔𝜑𝜓, 𝜓↗⋀¬𝜑¬𝜓] into ax-1
16756	→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓	Modus ponens 16752, 16755
16757	→→⋀¬𝜑¬𝜓→¬→¬𝜑¬¬𝜓↔𝜑𝜓→→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓↔𝜑𝜓	Subs [𝜑↗⋀¬𝜑¬𝜓, 𝜓↗¬→¬𝜑¬¬𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16758	→→⋀¬𝜑¬𝜓¬→¬𝜑¬¬𝜓→⋀¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 16756, 16757
16759	→⋀¬𝜑¬𝜓↔𝜑𝜓	Modus ponens 16754, 16758	pm5.21
16760	→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into pm5.1
16761	→→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒, 𝜓↗⋀→𝜑𝜓→𝜑𝜒] into ax-1
16762	→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 1905, 16761
16763	→→⋀→𝜑𝜓→𝜑𝜒→↔→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒→→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Subs [𝜑↗⋀→𝜑𝜓→𝜑𝜒, 𝜓↗↔→𝜑𝜓→𝜑𝜒, 𝜒↗→𝜑↔𝜓𝜒] into ax-2
16764	→→⋀→𝜑𝜓→𝜑𝜒↔→𝜑𝜓→𝜑𝜒→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 16762, 16763
16765	→⋀→𝜑𝜓→𝜑𝜒→𝜑↔𝜓𝜒	Modus ponens 16760, 16764	pm5.35
16766	↔→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓	Subs [𝜒↗→𝜑𝜓] into pm5.32
16767	→↔→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓→→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓	Subs [𝜑↗→𝜑↔𝜓→𝜑𝜓, 𝜓↗↔⋀𝜑𝜓⋀𝜑→𝜑𝜓] into biimp
16768	→→𝜑↔𝜓→𝜑𝜓↔⋀𝜑𝜓⋀𝜑→𝜑𝜓	Modus ponens 16766, 16767
16769	↔⋀𝜑𝜓⋀𝜑→𝜑𝜓	Modus ponens biimt, 16768	abai
16770	↔→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑	Subs [𝜓↗→𝜓𝜑] into pm4.71
16771	→↔→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑→→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑	Subs [𝜑↗→𝜑→𝜓𝜑, 𝜓↗↔𝜑⋀𝜑→𝜓𝜑] into biimp
16772	→→𝜑→𝜓𝜑↔𝜑⋀𝜑→𝜓𝜑	Modus ponens 16770, 16771
16773	↔𝜑⋀𝜑→𝜓𝜑	Modus ponens ax-1, 16772	pm4.45im
16774	→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into pm5.1
16775	→↔↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑] into biimp
16776	→→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔𝜑𝜓] into ax-1
16777	→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑	Modus ponens 16774, 16776
16778	→→↔𝜑𝜓→⋀→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗⋀→𝜑𝜓→𝜓𝜑, 𝜒↗↔→𝜑𝜓→𝜓𝜑] into ax-2
16779	→→↔𝜑𝜓⋀→𝜑𝜓→𝜓𝜑→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Modus ponens 16777, 16778
16780	→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Modus ponens 5712, 16779
16781	→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1
16782	→→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
16783	→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑	Modus ponens 16781, 16782
16784	→→¬→𝜑𝜓→→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→→¬→𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓→𝜓𝜑] into ax-2
16785	→→¬→𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑	Modus ponens 16783, 16784
16786	→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑	Modus ponens pm2.521, 16785
16787	→→𝜓𝜑¬¬→𝜓𝜑	Subs [𝜑↗→𝜓𝜑] into notnot
16788	→→→𝜓𝜑¬¬→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑¬¬→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-1
16789	→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑	Modus ponens 16787, 16788
16790	→→¬↔𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗¬¬→𝜓𝜑] into ax-2
16791	→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16789, 16790
16792	→→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑	Subs [𝜑↗→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
16793	→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16791, 16792
16794	→→¬→𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬¬→𝜓𝜑→→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬↔𝜑𝜓→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓¬¬→𝜓𝜑] into ax-2
16795	→→¬→𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16793, 16794
16796	→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16786, 16795
16797	→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-3
16798	→→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
16799	→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓	Modus ponens 16797, 16798
16800	→→¬→𝜑𝜓→→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬↔𝜑𝜓¬¬→𝜓𝜑, 𝜒↗→¬→𝜓𝜑↔𝜑𝜓] into ax-2
16801	→→¬→𝜑𝜓→¬↔𝜑𝜓¬¬→𝜓𝜑→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓	Modus ponens 16799, 16800
16802	→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓	Modus ponens 16796, 16801
16803	→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into biimpr
16804	→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑→→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜓𝜑] into ax-1
16805	→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Modus ponens 1674, 16804
16806	→→→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜓𝜑, 𝜒↗→→𝜑𝜓→𝜓𝜑] into ax-2
16807	→→→𝜓𝜑→𝜓𝜑→→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Modus ponens 16805, 16806
16808	→→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓, 𝜓↗→𝜓𝜑] into ax-1
16809	→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens 1681, 16808
16810	→→→𝜓𝜑→→→𝜑𝜓→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→𝜓𝜑, 𝜓↗→→𝜑𝜓→𝜓𝜑, 𝜒↗→→𝜑𝜓↔𝜑𝜓] into ax-2
16811	→→→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens 16809, 16810
16812	→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓	Modus ponens 1674, 16811
16813	→→→𝜓𝜑→→𝜑𝜓↔𝜑𝜓→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16814	→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Modus ponens 16812, 16813
16815	→→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16816	→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Modus ponens 16814, 16815
16817	→→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑→𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→→𝜓𝜑→𝜑𝜓, 𝜒↗→→𝜓𝜑↔𝜑𝜓] into ax-2
16818	→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓	Modus ponens 16816, 16817
16819	→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓	Modus ponens 16803, 16818
16820	→↔→𝜑𝜓→𝜓𝜑→→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜓𝜑] into biimp
16821	→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16822	→→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
16823	→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓	Modus ponens 16821, 16822
16824	→→¬¬→𝜑𝜓→→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓] into ax-2
16825	→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓	Modus ponens 16823, 16824
16826	→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓	Modus ponens 532, 16825
16827	→→↔→𝜑𝜓→𝜓𝜑→→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→𝜑𝜓, 𝜒↗→𝜓𝜑] into ax-2
16828	→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑	Modus ponens 16820, 16827
16829	→→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑	Subs [𝜑↗→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1
16830	→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑	Modus ponens 16828, 16829
16831	→→¬¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓, 𝜒↗→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑] into ax-2
16832	→→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜑𝜓→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑	Modus ponens 16830, 16831
16833	→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑	Modus ponens 16826, 16832
16834	→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑] into id
16835	→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1
16836	→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16837	→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Modus ponens 16835, 16836
16838	→→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑] into ax-2
16839	→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Modus ponens 16837, 16838
16840	→→¬¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗→𝜓𝜑] into ax-2
16841	→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑	Modus ponens 16833, 16840
16842	→→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16843	→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑	Modus ponens 16841, 16842
16844	→→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓→𝜓𝜑] into ax-2
16845	→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑	Modus ponens 16843, 16844
16846	→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑	Modus ponens 16835, 16845
16847	→→→𝜓𝜑¬¬→𝜓𝜑→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑	Subs [𝜑↗→→𝜓𝜑¬¬→𝜓𝜑, 𝜓↗¬¬→𝜑𝜓] into ax-1
16848	→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑	Modus ponens 16787, 16847
16849	→→¬¬→𝜑𝜓→→𝜓𝜑¬¬→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗¬¬→𝜓𝜑] into ax-2
16850	→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16848, 16849
16851	→→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑	Subs [𝜑↗→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16852	→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16850, 16851
16853	→→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓→𝜓𝜑, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜓𝜑] into ax-2
16854	→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16852, 16853
16855	→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑	Modus ponens 16846, 16854
16856	→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-3
16857	→→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16858	→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓	Modus ponens 16856, 16857
16859	→→↔→𝜑𝜓→𝜓𝜑→→¬¬→𝜑𝜓¬¬→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜓𝜑, 𝜒↗→¬→𝜓𝜑¬→𝜑𝜓] into ax-2
16860	→→↔→𝜑𝜓→𝜓𝜑→¬¬→𝜑𝜓¬¬→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓	Modus ponens 16858, 16859
16861	→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓	Modus ponens 16855, 16860
16862	→¬→𝜓𝜑¬→𝜓𝜑	Subs [𝜑↗¬→𝜓𝜑] into id
16863	→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓] into ax-1
16864	→→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑, 𝜓↗¬→𝜓𝜑] into ax-1
16865	→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑	Modus ponens 16863, 16864
16866	→→¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→→¬→𝜓𝜑¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑	Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜓𝜑, 𝜒↗→¬→𝜑𝜓¬→𝜓𝜑] into ax-2
16867	→→¬→𝜓𝜑¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑	Modus ponens 16865, 16866
16868	→→¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16869	→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓	Modus ponens 16802, 16868
16870	→→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-1
16871	→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓	Modus ponens 16869, 16870
16872	→→¬→𝜓𝜑→→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓	Subs [𝜑↗¬→𝜓𝜑, 𝜓↗→¬→𝜑𝜓¬→𝜓𝜑, 𝜒↗→¬→𝜑𝜓↔𝜑𝜓] into ax-2
16873	→→¬→𝜓𝜑→¬→𝜑𝜓¬→𝜓𝜑→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓	Modus ponens 16871, 16872
16874	→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓	Modus ponens 16863, 16873
16875	→→¬→𝜓𝜑→¬→𝜑𝜓↔𝜑𝜓→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗¬→𝜓𝜑, 𝜓↗¬→𝜑𝜓, 𝜒↗↔𝜑𝜓] into ax-2
16876	→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓	Modus ponens 16874, 16875
16877	→→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16878	→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓	Modus ponens 16876, 16877
16879	→→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬→𝜑𝜓→¬→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑¬→𝜑𝜓, 𝜒↗→¬→𝜓𝜑↔𝜑𝜓] into ax-2
16880	→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬→𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓	Modus ponens 16878, 16879
16881	→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓	Modus ponens 16861, 16880
16882	→→↔𝜑𝜓¬¬↔𝜑𝜓→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓	Subs [𝜑↗→↔𝜑𝜓¬¬↔𝜑𝜓, 𝜓↗¬→𝜓𝜑] into ax-1
16883	→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓	Modus ponens 16591, 16882
16884	→→¬→𝜓𝜑→↔𝜑𝜓¬¬↔𝜑𝜓→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓	Subs [𝜑↗¬→𝜓𝜑, 𝜓↗↔𝜑𝜓, 𝜒↗¬¬↔𝜑𝜓] into ax-2
16885	→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓	Modus ponens 16883, 16884
16886	→→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓	Subs [𝜑↗→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16887	→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓	Modus ponens 16885, 16886
16888	→→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑↔𝜑𝜓→¬→𝜓𝜑¬¬↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬→𝜓𝜑¬¬↔𝜑𝜓] into ax-2
16889	→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓	Modus ponens 16887, 16888
16890	→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓	Modus ponens 16881, 16889
16891	→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→𝜓𝜑, 𝜓↗¬↔𝜑𝜓] into ax-3
16892	→→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16893	→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑	Modus ponens 16891, 16892
16894	→→↔→𝜑𝜓→𝜓𝜑→→¬→𝜓𝜑¬¬↔𝜑𝜓→¬↔𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬→𝜓𝜑¬¬↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓→𝜓𝜑] into ax-2
16895	→→↔→𝜑𝜓→𝜓𝜑→¬→𝜓𝜑¬¬↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑	Modus ponens 16893, 16894
16896	→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑	Modus ponens 16890, 16895
16897	→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→𝜓𝜑↔𝜑𝜓, 𝜓↗¬↔𝜑𝜓] into ax-1
16898	→→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16899	→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Modus ponens 16897, 16898
16900	→→↔→𝜑𝜓→𝜓𝜑→→→𝜓𝜑↔𝜑𝜓→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→→𝜓𝜑↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓] into ax-2
16901	→→↔→𝜑𝜓→𝜓𝜑→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Modus ponens 16899, 16900
16902	→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓	Modus ponens 16819, 16901
16903	→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16904	→→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16905	→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Modus ponens 16903, 16904
16906	→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓, 𝜒↗→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓] into ax-2
16907	→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Modus ponens 16905, 16906
16908	→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Modus ponens 16902, 16907
16909	→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓→𝜓𝜑, 𝜒↗→¬↔𝜑𝜓↔𝜑𝜓] into ax-2
16910	→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Modus ponens 16908, 16909
16911	→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓	Modus ponens 16896, 16910
16912	→¬↔𝜑𝜓→↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗¬↔→𝜑𝜓→𝜓𝜑] into pm2.21
16913	→→¬↔𝜑𝜓→↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗¬↔𝜑𝜓, 𝜓↗↔𝜑𝜓, 𝜒↗¬↔→𝜑𝜓→𝜓𝜑] into ax-2
16914	→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Modus ponens 16912, 16913
16915	→→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16916	→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Modus ponens 16914, 16915
16917	→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓↔𝜑𝜓→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓↔𝜑𝜓, 𝜒↗→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑] into ax-2
16918	→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Modus ponens 16916, 16917
16919	→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑	Modus ponens 16911, 16918
16920	→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-3
16921	→→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into ax-1
16922	→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 16920, 16921
16923	→→↔→𝜑𝜓→𝜓𝜑→→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑, 𝜒↗→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓] into ax-2
16924	→→↔→𝜑𝜓→𝜓𝜑→¬↔𝜑𝜓¬↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 16922, 16923
16925	→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 16919, 16924
16926	→→↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Subs [𝜑↗↔→𝜑𝜓→𝜓𝜑, 𝜓↗↔→𝜑𝜓→𝜓𝜑, 𝜒↗↔𝜑𝜓] into ax-2
16927	→→↔→𝜑𝜓→𝜓𝜑↔→𝜑𝜓→𝜓𝜑→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 16925, 16926
16928	→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓	Modus ponens 16834, 16927
16929	→→↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑→→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Subs [𝜑↗↔𝜑𝜓, 𝜓↗↔→𝜑𝜓→𝜓𝜑] into impbi
16930	→→↔→𝜑𝜓→𝜓𝜑↔𝜑𝜓↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Modus ponens 16780, 16929
16931	↔↔𝜑𝜓↔→𝜑𝜓→𝜓𝜑	Modus ponens 16928, 16930	impimprbi
16932	↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒	Subs [𝜒↗¬𝜒] into impexp
16933	↔→𝜓¬𝜒¬⋀𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒] into imnan
16934	→↔→𝜓¬𝜒¬⋀𝜓𝜒→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒	Subs [𝜑↗↔→𝜓¬𝜒¬⋀𝜓𝜒, 𝜓↗𝜑] into ax-1
16935	→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒	Modus ponens 16933, 16934
16936	↔→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜓↗→𝜓¬𝜒, 𝜒↗¬⋀𝜓𝜒] into pm5.74
16937	→↔→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒, 𝜓↗↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒] into biimp
16938	→→𝜑↔→𝜓¬𝜒¬⋀𝜓𝜒↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16936, 16937
16939	↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16935, 16938
16940	→↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp
16941	→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16939, 16940
16942	→↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒	Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into biimp
16943	→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒	Modus ponens 16932, 16942
16944	→→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-1
16945	→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16941, 16944
16946	→→→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒, 𝜒↗→𝜑¬⋀𝜓𝜒] into ax-2
16947	→→→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16945, 16946
16948	→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16943, 16947
16949	→↔→𝜑→𝜓¬𝜒→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒	Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1
16950	↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒	Modus ponens 16939, 16949
16951	→↔→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒	Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into biimp
16952	→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒	Modus ponens 16950, 16951
16953	→↔→⋀𝜑𝜓¬𝜒→𝜑→𝜓¬𝜒↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑→𝜓¬𝜒] into bicom1
16954	↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 16932, 16953
16955	→↔→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→𝜑→𝜓¬𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into biimp
16956	→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 16954, 16955
16957	→→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into ax-1
16958	→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 16956, 16957
16959	→→→𝜑¬⋀𝜓𝜒→→𝜑→𝜓¬𝜒→⋀𝜑𝜓¬𝜒→→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→𝜑→𝜓¬𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
16960	→→→𝜑¬⋀𝜓𝜒→𝜑→𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 16958, 16959
16961	→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 16952, 16960
16962	→→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into impbi
16963	→→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16948, 16962
16964	↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Modus ponens 16961, 16963
16965	→↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1
16966	↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 16964, 16965	nan
16967	→⋀𝜒→𝜑𝜓→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into simpr
16968	→⋀𝜒→𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into simpl
16969	→→𝜒→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒	Subs [𝜑↗→𝜒→𝜑𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
16970	→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒	Modus ponens 1834, 16969
16971	→→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑𝜒	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜒] into ax-2
16972	→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 16970, 16971
16973	→⋀𝜒→𝜑𝜓→𝜑𝜒	Modus ponens 16968, 16972
16974	→→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
16975	→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 5594, 16974
16976	→→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑→𝜒⋀𝜓𝜒] into ax-2
16977	→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 16975, 16976
16978	→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒	Modus ponens 16967, 16977
16979	→→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
16980	→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 5595, 16979
16981	→→⋀𝜒→𝜑𝜓→→𝜑→𝜒⋀𝜓𝜒→→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑→𝜒⋀𝜓𝜒, 𝜒↗→→𝜑𝜒→𝜑⋀𝜓𝜒] into ax-2
16982	→→⋀𝜒→𝜑𝜓→𝜑→𝜒⋀𝜓𝜒→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 16980, 16981
16983	→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒	Modus ponens 16978, 16982
16984	→→⋀𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜓𝜒→→⋀𝜒→𝜑𝜓→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜓𝜒] into ax-2
16985	→→⋀𝜒→𝜑𝜓→𝜑𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 16983, 16984
16986	→⋀𝜒→𝜑𝜓→𝜑⋀𝜓𝜒	Modus ponens 16973, 16985	pm5.31
16987	→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜓↗𝜒, 𝜒↗𝜓] into pm3.43
16988	↔⋀→𝜑𝜒→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into df-an
16989	→↔⋀→𝜑𝜒→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓	Subs [𝜑↗⋀→𝜑𝜒→𝜑𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓] into bicom1
16990	↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓	Modus ponens 16988, 16989
16991	→↔¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓	Subs [𝜑↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜓↗⋀→𝜑𝜒→𝜑𝜓] into biimp
16992	→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓	Modus ponens 16990, 16991
16993	→→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓] into ax-1
16994	→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 16987, 16993
16995	→→¬→→𝜑𝜒¬→𝜑𝜓→⋀→𝜑𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜓↗⋀→𝜑𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
16996	→→¬→→𝜑𝜒¬→𝜑𝜓⋀→𝜑𝜒→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 16994, 16995
16997	→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 16992, 16996
16998	→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓] into pm3.2im
16999	→→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17000	→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 16997, 16999
17001	→→→𝜑𝜓→¬→→𝜑𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜑𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17002	→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17000, 17001
17003	→→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜒] into ax-1
17004	→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17002, 17003
17005	→→→𝜑𝜒→→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜒, 𝜓↗→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17006	→→→𝜑𝜒→→𝜑𝜓¬→→𝜑𝜒¬→𝜑𝜓→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17004, 17005
17007	→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 16998, 17006
17008	→→𝜑𝜓→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒] into ax-1
17009	→→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→→𝜑𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17010	→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓	Modus ponens 17008, 17009
17011	→→→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→→𝜑𝜒→𝜑𝜓] into ax-2
17012	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑𝜓	Modus ponens 17010, 17011
17013	→→→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17014	→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓	Modus ponens 17007, 17013
17015	→→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17016	→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓	Modus ponens 17014, 17015
17017	→→→𝜑𝜓→→→𝜑𝜒→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→→𝜑𝜒→𝜑𝜓, 𝜒↗→→𝜑𝜒→𝜑⋀𝜒𝜓] into ax-2
17018	→→→𝜑𝜓→→𝜑𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓	Modus ponens 17016, 17017
17019	→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓	Modus ponens 17008, 17018
17020	→→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗→→𝜑𝜒→→𝜑𝜓→𝜑𝜒, 𝜓↗𝜒] into ax-1
17021	→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 5603, 17020
17022	→→𝜒→→𝜑𝜒→→𝜑𝜓→𝜑𝜒→→𝜒→𝜑𝜒→𝜒→→𝜑𝜓→𝜑𝜒	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜒] into ax-2
17023	→→𝜒→𝜑𝜒→𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 17021, 17022
17024	→𝜒→→𝜑𝜓→𝜑𝜒	Modus ponens 1834, 17023
17025	→→→𝜑𝜓→→𝜑𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17026	→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17019, 17025
17027	→→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17028	→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17026, 17027
17029	→→𝜒→→→𝜑𝜓→𝜑𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓→𝜑𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17030	→→𝜒→→𝜑𝜓→𝜑𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17028, 17029
17031	→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17024, 17030
17032	→→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17033	→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17031, 17032
17034	→→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17035	→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17033, 17034
17036	→→→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2
17037	→→→𝜑𝜓→𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17035, 17036
17038	→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 39, 17037
17039	→→→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17040	→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17038, 17039
17041	→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17042	→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17040, 17041
17043	→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17044	→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17042, 17043
17045	↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into df-an
17046	→→→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17047	→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 39, 17046
17048	→→¬¬→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17049	→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 17047, 17048
17050	→¬¬→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 532, 17049
17051	→→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17052	→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17033, 17051
17053	→→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2
17054	→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17052, 17053
17055	→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17050, 17054
17056	→𝜒→¬¬→𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗¬¬→𝜑𝜓] into ax-1
17057	→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→𝜒→¬¬→𝜑𝜓𝜒	Subs [𝜑↗→𝜒→¬¬→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
17058	→𝜒→𝜒→¬¬→𝜑𝜓𝜒	Modus ponens 17056, 17057
17059	→→𝜒→𝜒→¬¬→𝜑𝜓𝜒→→𝜒𝜒→𝜒→¬¬→𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→¬¬→𝜑𝜓𝜒] into ax-2
17060	→→𝜒𝜒→𝜒→¬¬→𝜑𝜓𝜒	Modus ponens 17058, 17059
17061	→→¬¬→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17062	→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17055, 17061
17063	→→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17064	→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17062, 17063
17065	→→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17066	→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17064, 17065
17067	→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17056, 17066
17068	→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑⋀𝜒𝜓] into notnot
17069	→→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓	Subs [𝜑↗→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17070	→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓	Modus ponens 17068, 17069
17071	→→¬¬→𝜑𝜓→→𝜑⋀𝜒𝜓¬¬→𝜑⋀𝜒𝜓→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑⋀𝜒𝜓, 𝜒↗¬¬→𝜑⋀𝜒𝜓] into ax-2
17072	→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓	Modus ponens 17070, 17071
17073	→→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17074	→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓	Modus ponens 17072, 17073
17075	→→𝜒→→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓] into ax-2
17076	→→𝜒→¬¬→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓	Modus ponens 17074, 17075
17077	→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓	Modus ponens 17067, 17076
17078	→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-3
17079	→→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17080	→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓	Modus ponens 17078, 17079
17081	→→𝜒→→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓] into ax-2
17082	→→𝜒→¬¬→𝜑𝜓¬¬→𝜑⋀𝜒𝜓→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓	Modus ponens 17080, 17081
17083	→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓	Modus ponens 17077, 17082
17084	→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓] into id
17085	→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17086	→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓	Subs [𝜑↗→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17087	→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓	Modus ponens 17085, 17086
17088	→→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗→𝜒¬→𝜑⋀𝜒𝜓] into ax-2
17089	→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓	Modus ponens 17087, 17088
17090	→→𝜒→¬→𝜑⋀𝜒𝜓¬→𝜑𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
17091	→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓	Modus ponens 17083, 17090
17092	→→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17093	→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓	Modus ponens 17091, 17092
17094	→→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→𝜒¬→𝜑⋀𝜒𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2
17095	→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓	Modus ponens 17093, 17094
17096	→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓	Modus ponens 17085, 17095
17097	→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜒¬→𝜑𝜓] into id
17098	→→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17099	→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17097, 17098
17100	→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜒¬→𝜑𝜓] into notnotr
17101	→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17102	→→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17103	→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17101, 17102
17104	→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17105	→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17103, 17104
17106	→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17100, 17105
17107	→→¬→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17108	→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17099, 17107
17109	→→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17110	→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17108, 17109
17111	→→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17112	→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17110, 17111
17113	→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17114	→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓	Subs [𝜑↗→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17115	→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓	Modus ponens 17113, 17114
17116	→→¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓] into ax-2
17117	→→¬→𝜑⋀𝜒𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓	Modus ponens 17115, 17116
17118	→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17119	→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17106, 17118
17120	→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17121	→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17119, 17120
17122	→→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17123	→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑⋀𝜒𝜓→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17121, 17122
17124	→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17113, 17123
17125	→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬→𝜒¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓] into ax-3
17126	→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑⋀𝜒𝜓] into ax-1
17127	→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17125, 17126
17128	→→¬→𝜑⋀𝜒𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓] into ax-2
17129	→→¬→𝜑⋀𝜒𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17127, 17128
17130	→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17124, 17129
17131	→→¬→𝜑⋀𝜒𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑⋀𝜒𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗¬¬→𝜒¬→𝜑𝜓] into ax-2
17132	→→¬→𝜑⋀𝜒𝜓→𝜒¬→𝜑𝜓→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17130, 17131
17133	→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17096, 17132
17134	→→¬→𝜑⋀𝜒𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-3
17135	→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17133, 17134
17136	→↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into biimp
17137	→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17045, 17136
17138	→→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17139	→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17135, 17138
17140	→→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17141	→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17139, 17140
17142	→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17137, 17141	pm5.31r
17143	↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into df-an
17144	→→𝜒→→𝜑𝜓𝜒→¬¬𝜒→𝜒→→𝜑𝜓𝜒	Subs [𝜑↗→𝜒→→𝜑𝜓𝜒, 𝜓↗¬¬𝜒] into ax-1
17145	→¬¬𝜒→𝜒→→𝜑𝜓𝜒	Modus ponens 7185, 17144
17146	→→¬¬𝜒→𝜒→→𝜑𝜓𝜒→→¬¬𝜒𝜒→¬¬𝜒→→𝜑𝜓𝜒	Subs [𝜑↗¬¬𝜒, 𝜓↗𝜒, 𝜒↗→→𝜑𝜓𝜒] into ax-2
17147	→→¬¬𝜒𝜒→¬¬𝜒→→𝜑𝜓𝜒	Modus ponens 17145, 17146
17148	→¬¬𝜒→→𝜑𝜓𝜒	Modus ponens 5153, 17147
17149	→→→𝜑𝜓→𝜒→𝜑𝜓→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜓] into ax-2
17150	→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 39, 17149
17151	→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
17152	→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 17150, 17151
17153	→→¬¬𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→→¬¬𝜒→→𝜑𝜓𝜒→¬¬𝜒→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗¬¬𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜓] into ax-2
17154	→→¬¬𝜒→→𝜑𝜓𝜒→¬¬𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 17152, 17153
17155	→¬¬𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 17148, 17154
17156	→→𝜑𝜓→¬¬𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
17157	→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→¬¬𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17158	→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓	Modus ponens 17156, 17157
17159	→→→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→¬¬𝜒→𝜑𝜓] into ax-2
17160	→→→𝜑𝜓→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓	Modus ponens 17158, 17159
17161	→→¬¬𝜒→→𝜑𝜓→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17162	→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓	Modus ponens 17155, 17161
17163	→→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓	Subs [𝜑↗→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17164	→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓	Modus ponens 17162, 17163
17165	→→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒→𝜑𝜓→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒→𝜑𝜓, 𝜒↗→¬¬𝜒→𝜑𝜓] into ax-2
17166	→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒→𝜑𝜓	Modus ponens 17164, 17165
17167	→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗→𝜑𝜓] into notnot
17168	→→→𝜑𝜓¬¬→𝜑𝜓→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬𝜒] into ax-1
17169	→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 17167, 17168
17170	→→¬¬𝜒→→𝜑𝜓¬¬→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓	Subs [𝜑↗¬¬𝜒, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
17171	→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓	Modus ponens 17169, 17170
17172	→→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓	Subs [𝜑↗→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17173	→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓	Modus ponens 17171, 17172
17174	→→→𝜑𝜓→→¬¬𝜒→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒→𝜑𝜓, 𝜒↗→¬¬𝜒¬¬→𝜑𝜓] into ax-2
17175	→→→𝜑𝜓→¬¬𝜒→𝜑𝜓→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓	Modus ponens 17173, 17174
17176	→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓	Modus ponens 17156, 17175
17177	→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒	Subs [𝜑↗¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-3
17178	→→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒, 𝜓↗→𝜑𝜓] into ax-1
17179	→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒	Modus ponens 17177, 17178
17180	→→→𝜑𝜓→→¬¬𝜒¬¬→𝜑𝜓→¬→𝜑𝜓¬𝜒→→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→¬→𝜑𝜓¬𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗→¬¬𝜒¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬𝜒] into ax-2
17181	→→→𝜑𝜓→¬¬𝜒¬¬→𝜑𝜓→→𝜑𝜓→¬→𝜑𝜓¬𝜒	Modus ponens 17179, 17180
17182	→→𝜑𝜓→¬→𝜑𝜓¬𝜒	Modus ponens 17176, 17181
17183	→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17184	→→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17185	→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓	Modus ponens 17183, 17184
17186	→→¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬→𝜑𝜓] into ax-2
17187	→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓	Modus ponens 17185, 17186
17188	→→→𝜑𝜓→¬→𝜑𝜓¬𝜒→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬𝜒] into ax-2
17189	→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒	Modus ponens 17182, 17188
17190	→→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒	Subs [𝜑↗→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17191	→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒	Modus ponens 17189, 17190
17192	→→¬→𝜑𝜓→→→𝜑𝜓¬→𝜑𝜓→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→→𝜑𝜓¬→𝜑𝜓, 𝜒↗→→𝜑𝜓¬𝜒] into ax-2
17193	→→¬→𝜑𝜓→→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→→𝜑𝜓¬𝜒	Modus ponens 17191, 17192
17194	→¬→𝜑𝜓→→𝜑𝜓¬𝜒	Modus ponens 17183, 17193
17195	→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓¬𝜒] into id
17196	→→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17197	→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Modus ponens 17195, 17196
17198	→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓¬𝜒] into notnotr
17199	→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17200	→→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1
17201	→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Modus ponens 17199, 17200
17202	→→¬¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒] into ax-2
17203	→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Modus ponens 17201, 17202
17204	→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Modus ponens 17198, 17203
17205	→→¬→𝜑𝜓→¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗¬→→𝜑𝜓¬𝜒] into ax-2
17206	→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Modus ponens 17197, 17205
17207	→→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Subs [𝜑↗→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1
17208	→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Modus ponens 17206, 17207
17209	→→¬¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒, 𝜒↗→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒] into ax-2
17210	→→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒	Modus ponens 17208, 17209
17211	→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬¬→→𝜑𝜓¬𝜒] into ax-1
17212	→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17213	→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓	Modus ponens 17211, 17212
17214	→→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓] into ax-2
17215	→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓	Modus ponens 17213, 17214
17216	→→¬¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬→→𝜑𝜓¬𝜒→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→→𝜑𝜓¬𝜒] into ax-2
17217	→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Modus ponens 17204, 17216
17218	→→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17219	→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Modus ponens 17217, 17218
17220	→→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓, 𝜒↗→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒] into ax-2
17221	→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Modus ponens 17219, 17220
17222	→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒	Modus ponens 17211, 17221
17223	→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬¬→→𝜑𝜓¬𝜒, 𝜓↗→→𝜑𝜓¬𝜒] into ax-3
17224	→→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒	Subs [𝜑↗→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒, 𝜓↗¬→𝜑𝜓] into ax-1
17225	→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒	Modus ponens 17223, 17224
17226	→→¬→𝜑𝜓→→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒, 𝜒↗→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒] into ax-2
17227	→→¬→𝜑𝜓→¬¬¬→→𝜑𝜓¬𝜒¬→→𝜑𝜓¬𝜒→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒	Modus ponens 17225, 17226
17228	→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒	Modus ponens 17222, 17227
17229	→→¬→𝜑𝜓→→→𝜑𝜓¬𝜒¬¬→→𝜑𝜓¬𝜒→→¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→→𝜑𝜓¬𝜒, 𝜒↗¬¬→→𝜑𝜓¬𝜒] into ax-2
17230	→→¬→𝜑𝜓→→𝜑𝜓¬𝜒→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒	Modus ponens 17228, 17229
17231	→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒	Modus ponens 17194, 17230
17232	→→¬→𝜑𝜓¬¬→→𝜑𝜓¬𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒] into ax-3
17233	→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Modus ponens 17231, 17232
17234	→↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒] into biimp
17235	→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒	Modus ponens 17143, 17234
17236	→→¬→→𝜑𝜓¬𝜒→𝜑𝜓→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→𝜑𝜓, 𝜓↗⋀→𝜑𝜓𝜒] into ax-1
17237	→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Modus ponens 17233, 17236
17238	→→⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓→→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜑𝜓] into ax-2
17239	→→⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 17237, 17238
17240	→⋀→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 17235, 17239
17241	→↔⋀→𝜑𝜓𝜒¬→→𝜑𝜓¬𝜒↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒	Subs [𝜑↗⋀→𝜑𝜓𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒] into bicom1
17242	↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒	Modus ponens 17143, 17241
17243	→↔¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒	Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗⋀→𝜑𝜓𝜒] into biimp
17244	→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒	Modus ponens 17242, 17243
17245	→→⋀→𝜑𝜓𝜒→𝜑𝜓→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓	Subs [𝜑↗→⋀→𝜑𝜓𝜒→𝜑𝜓, 𝜓↗¬→→𝜑𝜓¬𝜒] into ax-1
17246	→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓	Modus ponens 17240, 17245
17247	→→¬→→𝜑𝜓¬𝜒→⋀→𝜑𝜓𝜒→𝜑𝜓→→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Subs [𝜑↗¬→→𝜑𝜓¬𝜒, 𝜓↗⋀→𝜑𝜓𝜒, 𝜒↗→𝜑𝜓] into ax-2
17248	→→¬→→𝜑𝜓¬𝜒⋀→𝜑𝜓𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Modus ponens 17246, 17247
17249	→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒	Subs [𝜑↗→𝜑𝜓, 𝜓↗𝜒] into pm3.2im
17250	→→¬→→𝜑𝜓¬𝜒→𝜑𝜓→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Subs [𝜑↗→¬→→𝜑𝜓¬𝜒→𝜑𝜓, 𝜓↗𝜒] into ax-1
17251	→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓	Modus ponens 17233, 17250
17252	→→𝜒→¬→→𝜑𝜓¬𝜒→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜑𝜓] into ax-2
17253	→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓	Modus ponens 17251, 17252
17254	→→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓	Subs [𝜑↗→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17255	→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓	Modus ponens 17253, 17254
17256	→→→𝜑𝜓→→𝜒¬→→𝜑𝜓¬𝜒→𝜒→𝜑𝜓→→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒→→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜒¬→→𝜑𝜓¬𝜒, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17257	→→→𝜑𝜓→𝜒¬→→𝜑𝜓¬𝜒→→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 17255, 17256
17258	→→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓, 𝜓↗𝜒] into ax-1
17259	→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 17150, 17258
17260	→→𝜒→→→𝜑𝜓𝜒→→𝜑𝜓→𝜑𝜓→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓𝜒, 𝜒↗→→𝜑𝜓→𝜑𝜓] into ax-2
17261	→→𝜒→→𝜑𝜓𝜒→𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 17259, 17260
17262	→𝜒→→𝜑𝜓→𝜑𝜓	Modus ponens 7185, 17261
17263	→→𝜒→→𝜑𝜓→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17264	→→𝜒→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 17262, 17263
17265	→→→𝜒→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17266	→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 17264, 17265
17267	→→¬¬→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17268	→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→¬¬→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 17266, 17267
17269	→→¬¬→𝜑𝜓→𝜒→𝜑𝜓→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑𝜓] into ax-2
17270	→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓	Modus ponens 17050, 17269
17271	→→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓, 𝜓↗𝜒] into ax-1
17272	→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓	Modus ponens 17270, 17271
17273	→→𝜒→→¬¬→𝜑𝜓𝜒→¬¬→𝜑𝜓→𝜑𝜓→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓𝜒, 𝜒↗→¬¬→𝜑𝜓→𝜑𝜓] into ax-2
17274	→→𝜒→¬¬→𝜑𝜓𝜒→𝜒→¬¬→𝜑𝜓→𝜑𝜓	Modus ponens 17272, 17273
17275	→𝜒→¬¬→𝜑𝜓→𝜑𝜓	Modus ponens 17056, 17274
17276	→→→𝜑𝜓¬¬→𝜑𝜓→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗¬¬→𝜑𝜓] into ax-1
17277	→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 17167, 17276
17278	→→¬¬→𝜑𝜓→→𝜑𝜓¬¬→𝜑𝜓→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗¬¬→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗¬¬→𝜑𝜓] into ax-2
17279	→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 17277, 17278
17280	→→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17281	→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 17279, 17280
17282	→→𝜒→→¬¬→𝜑𝜓→𝜑𝜓→¬¬→𝜑𝜓¬¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓→𝜑𝜓, 𝜒↗→¬¬→𝜑𝜓¬¬→𝜑𝜓] into ax-2
17283	→→𝜒→¬¬→𝜑𝜓→𝜑𝜓→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 17281, 17282
17284	→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓	Modus ponens 17275, 17283
17285	→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-3
17286	→→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17287	→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 17285, 17286
17288	→→𝜒→→¬¬→𝜑𝜓¬¬→𝜑𝜓→¬→𝜑𝜓¬→𝜑𝜓→→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→¬¬→𝜑𝜓¬¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜑𝜓] into ax-2
17289	→→𝜒→¬¬→𝜑𝜓¬¬→𝜑𝜓→𝜒→¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 17287, 17288
17290	→𝜒→¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 17284, 17289
17291	→¬→𝜑𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗𝜒] into ax-1
17292	→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17293	→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓	Modus ponens 17291, 17292
17294	→→¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2
17295	→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓	Modus ponens 17293, 17294
17296	→→𝜒→¬→𝜑𝜓¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜑𝜓] into ax-2
17297	→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓	Modus ponens 17290, 17296
17298	→→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17299	→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓	Modus ponens 17297, 17298
17300	→→¬→𝜑𝜓→→𝜒¬→𝜑𝜓→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗→𝜒¬→𝜑𝜓] into ax-2
17301	→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓→𝜒¬→𝜑𝜓	Modus ponens 17299, 17300
17302	→→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17303	→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17097, 17302
17304	→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17305	→→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17306	→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17304, 17305
17307	→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17308	→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17306, 17307
17309	→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17100, 17308
17310	→→¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17311	→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17303, 17310
17312	→→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17313	→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17311, 17312
17314	→→¬¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17315	→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17313, 17314
17316	→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬¬¬→𝜒¬→𝜑𝜓] into ax-1
17317	→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17318	→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 17316, 17317
17319	→→¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓] into ax-2
17320	→→¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓	Modus ponens 17318, 17319
17321	→→¬¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓, 𝜒↗¬→𝜒¬→𝜑𝜓] into ax-2
17322	→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17309, 17321
17323	→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17324	→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17322, 17323
17325	→→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓, 𝜒↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓] into ax-2
17326	→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜑𝜓→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17324, 17325
17327	→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓	Modus ponens 17316, 17326
17328	→→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Subs [𝜑↗→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓, 𝜓↗¬→𝜑𝜓] into ax-1
17329	→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17125, 17328
17330	→→¬→𝜑𝜓→→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓] into ax-2
17331	→→¬→𝜑𝜓→¬¬¬→𝜒¬→𝜑𝜓¬→𝜒¬→𝜑𝜓→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17329, 17330
17332	→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17327, 17331
17333	→→¬→𝜑𝜓→→𝜒¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Subs [𝜑↗¬→𝜑𝜓, 𝜓↗→𝜒¬→𝜑𝜓, 𝜒↗¬¬→𝜒¬→𝜑𝜓] into ax-2
17334	→→¬→𝜑𝜓→𝜒¬→𝜑𝜓→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17332, 17333
17335	→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓	Modus ponens 17291, 17334
17336	→→¬→𝜑𝜓¬¬→𝜒¬→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-3
17337	→¬→𝜒¬→𝜑𝜓→𝜑𝜓	Modus ponens 17335, 17336
17338	→→¬→𝜒¬→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓	Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17339	→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓	Modus ponens 17337, 17338
17340	→→⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑𝜓→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17341	→→⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑𝜓	Modus ponens 17339, 17340
17342	→↔⋀𝜒→𝜑𝜓¬→𝜒¬→𝜑𝜓↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into bicom1
17343	↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓	Modus ponens 17045, 17342
17344	→↔¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓	Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into biimp
17345	→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓	Modus ponens 17343, 17344
17346	→→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓] into ax-1
17347	→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens pm5.31r, 17346
17348	→→¬→𝜒¬→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗¬→𝜒¬→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17349	→→¬→𝜒¬→𝜑𝜓⋀𝜒→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17347, 17348
17350	→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓	Subs [𝜑↗𝜒, 𝜓↗→𝜑𝜓] into pm3.2im
17351	→→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗→𝜑𝜓] into ax-1
17352	→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17135, 17351
17353	→→→𝜑𝜓→¬→𝜒¬→𝜑𝜓→𝜑⋀𝜒𝜓→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗¬→𝜒¬→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17354	→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17352, 17353
17355	→→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17356	→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17354, 17355
17357	→→𝜒→→→𝜑𝜓¬→𝜒¬→𝜑𝜓→→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗→→𝜑𝜓¬→𝜒¬→𝜑𝜓, 𝜒↗→→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17358	→→𝜒→→𝜑𝜓¬→𝜒¬→𝜑𝜓→𝜒→→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17356, 17357
17359	→→→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜒→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17360	→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 39, 17359
17361	→→⋀𝜒→𝜑𝜓→→𝜑𝜓→𝜒→𝜑𝜓→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜒→𝜑𝜓] into ax-2
17362	→→⋀𝜒→𝜑𝜓→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 17360, 17361
17363	→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓	Modus ponens 16967, 17362
17364	→→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17365	→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17033, 17364
17366	→→⋀𝜒→𝜑𝜓→→𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗→𝜒→𝜑𝜓, 𝜒↗→𝜒→𝜑⋀𝜒𝜓] into ax-2
17367	→→⋀𝜒→𝜑𝜓→𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17365, 17366
17368	→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓	Modus ponens 17363, 17367
17369	→𝜒→⋀𝜒→𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17370	→→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒	Subs [𝜑↗→𝜒→⋀𝜒→𝜑𝜓𝜒, 𝜓↗𝜒] into ax-1
17371	→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒	Modus ponens 17369, 17370
17372	→→𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒→→𝜒𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒	Subs [𝜑↗𝜒, 𝜓↗𝜒, 𝜒↗→⋀𝜒→𝜑𝜓𝜒] into ax-2
17373	→→𝜒𝜒→𝜒→⋀𝜒→𝜑𝜓𝜒	Modus ponens 17371, 17372
17374	→→⋀𝜒→𝜑𝜓→𝜒→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17375	→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17368, 17374
17376	→→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗𝜒] into ax-1
17377	→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17375, 17376
17378	→→𝜒→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗𝜒, 𝜓↗→⋀𝜒→𝜑𝜓𝜒, 𝜒↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17379	→→𝜒→⋀𝜒→𝜑𝜓𝜒→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17377, 17378
17380	→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17369, 17379
17381	→→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓, 𝜓↗⋀𝜒→𝜑𝜓] into ax-1
17382	→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17380, 17381
17383	→→⋀𝜒→𝜑𝜓→𝜒→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗𝜒, 𝜒↗→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓] into ax-2
17384	→→⋀𝜒→𝜑𝜓𝜒→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17382, 17383
17385	→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 16968, 17384
17386	→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓] into id
17387	→→⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓→→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Subs [𝜑↗⋀𝜒→𝜑𝜓, 𝜓↗⋀𝜒→𝜑𝜓, 𝜒↗→𝜑⋀𝜒𝜓] into ax-2
17388	→→⋀𝜒→𝜑𝜓⋀𝜒→𝜑𝜓→⋀𝜒→𝜑𝜓→𝜑⋀𝜒𝜓	Modus ponens 17385, 17387
17389	↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒	Subs [𝜑↗⋀𝜓𝜒, 𝜓↗𝜑] into con2b
17390	→↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into biimp
17391	→↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp
17392	→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒	Modus ponens 17389, 17391
17393	→→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑] into ax-1
17394	→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒	Modus ponens 16961, 17393
17395	→→→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒→→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜑𝜓¬𝜒] into ax-2
17396	→→→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 17394, 17395
17397	→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 17392, 17396
17398	→↔→𝜑¬⋀𝜓𝜒→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜑𝜓¬𝜒] into bicom1
17399	→↔→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒] into biimp
17400	→↔→⋀𝜓𝜒¬𝜑→𝜑¬⋀𝜓𝜒↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→𝜑¬⋀𝜓𝜒] into bicom1
17401	↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 17389, 17400
17402	→↔→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→𝜑¬⋀𝜓𝜒, 𝜓↗→⋀𝜓𝜒¬𝜑] into biimp
17403	→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 17401, 17402
17404	→→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into ax-1
17405	→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 17403, 17404
17406	→→→⋀𝜑𝜓¬𝜒→→𝜑¬⋀𝜓𝜒→⋀𝜓𝜒¬𝜑→→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→⋀𝜑𝜓¬𝜒, 𝜓↗→𝜑¬⋀𝜓𝜒, 𝜒↗→⋀𝜓𝜒¬𝜑] into ax-2
17407	→→→⋀𝜑𝜓¬𝜒→𝜑¬⋀𝜓𝜒→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 17405, 17406
17408	→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 16948, 17407
17409	→→→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒→→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒	Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into impbi
17410	→→→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 17397, 17409
17411	↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒	Modus ponens 17408, 17410
17412	→↔→⋀𝜓𝜒¬𝜑→⋀𝜑𝜓¬𝜒↔→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑	Subs [𝜑↗→⋀𝜓𝜒¬𝜑, 𝜓↗→⋀𝜑𝜓¬𝜒] into bicom1
17413	↔→⋀𝜑𝜓¬𝜒→⋀𝜓𝜒¬𝜑	Modus ponens 17411, 17412	pm4.15
17414	↔→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓	Subs [𝜑↗↔𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into pm5.32
17415	→↔→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓	Subs [𝜑↗→↔𝜑𝜓↔𝜑𝜓, 𝜓↗↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓] into biimp
17416	→→↔𝜑𝜓↔𝜑𝜓↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓	Modus ponens 17414, 17415
17417	↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓	Modus ponens 1651, 17416
17418	↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑	Subs [𝜓↗↔𝜑𝜓] into ancom
17419	↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓	Subs [𝜑↗𝜓, 𝜓↗↔𝜑𝜓] into ancom
17420	→↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓	Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓] into bicom1
17421	↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓	Modus ponens 17419, 17420
17422	→↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓	Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into biimp
17423	→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓	Modus ponens 17421, 17422
17424	→↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓	Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓] into biimp
17425	→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓	Modus ponens 17417, 17424
17426	→→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into ax-1
17427	→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓	Modus ponens 17423, 17426
17428	→→⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓→→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓, 𝜒↗⋀𝜓↔𝜑𝜓] into ax-2
17429	→→⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Modus ponens 17427, 17428
17430	→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Modus ponens 17425, 17429
17431	→↔⋀↔𝜑𝜓𝜓⋀𝜓↔𝜑𝜓↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓	Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into bicom1
17432	→↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓	Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓] into biimp
17433	→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓	Modus ponens 17419, 17432
17434	→↔⋀↔𝜑𝜓𝜑⋀↔𝜑𝜓𝜓↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑	Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀↔𝜑𝜓𝜓] into bicom1
17435	↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑	Modus ponens 17417, 17434
17436	→↔⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑	Subs [𝜑↗⋀↔𝜑𝜓𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp
17437	→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑	Modus ponens 17435, 17436
17438	→→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑	Subs [𝜑↗→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into ax-1
17439	→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑	Modus ponens 17437, 17438
17440	→→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜓⋀↔𝜑𝜓𝜑→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑	Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜓, 𝜒↗⋀↔𝜑𝜓𝜑] into ax-2
17441	→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜓→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑	Modus ponens 17439, 17440
17442	→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑	Modus ponens 17433, 17441
17443	→→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into impbi
17444	→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Modus ponens 17430, 17443
17445	↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Modus ponens 17442, 17444
17446	→↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into biimp
17447	→↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑	Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp
17448	→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑	Modus ponens 17418, 17447
17449	→→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓, 𝜓↗⋀𝜑↔𝜑𝜓] into ax-1
17450	→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓	Modus ponens 17430, 17449
17451	→→⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓→→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓	Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑, 𝜒↗⋀𝜓↔𝜑𝜓] into ax-2
17452	→→⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓	Modus ponens 17450, 17451
17453	→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓	Modus ponens 17448, 17452
17454	→↔⋀↔𝜑𝜓𝜑⋀𝜓↔𝜑𝜓↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑	Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜓↔𝜑𝜓] into bicom1
17455	↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑	Modus ponens 17445, 17454
17456	→↔⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑	Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into biimp
17457	→↔⋀𝜑↔𝜑𝜓⋀↔𝜑𝜓𝜑↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓	Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑] into bicom1
17458	↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓	Modus ponens 17418, 17457
17459	→↔⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓	Subs [𝜑↗⋀↔𝜑𝜓𝜑, 𝜓↗⋀𝜑↔𝜑𝜓] into biimp
17460	→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓	Modus ponens 17458, 17459
17461	→→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓	Subs [𝜑↗→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into ax-1
17462	→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓	Modus ponens 17460, 17461
17463	→→⋀𝜓↔𝜑𝜓→⋀↔𝜑𝜓𝜑⋀𝜑↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓	Subs [𝜑↗⋀𝜓↔𝜑𝜓, 𝜓↗⋀↔𝜑𝜓𝜑, 𝜒↗⋀𝜑↔𝜑𝜓] into ax-2
17464	→→⋀𝜓↔𝜑𝜓⋀↔𝜑𝜓𝜑→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓	Modus ponens 17462, 17463
17465	→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓	Modus ponens 17442, 17464
17466	→→⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓→→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓	Subs [𝜑↗⋀𝜑↔𝜑𝜓, 𝜓↗⋀𝜓↔𝜑𝜓] into impbi
17467	→→⋀𝜓↔𝜑𝜓⋀𝜑↔𝜑𝜓↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓	Modus ponens 17453, 17466
17468	↔⋀𝜑↔𝜑𝜓⋀𝜓↔𝜑𝜓	Modus ponens 17465, 17467	pm5.36
17469	↔⋀𝜑𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓] into notnotb
17470	→↔⋀𝜑𝜓¬¬⋀𝜑𝜓↔¬¬⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗¬¬⋀𝜑𝜓] into bicom1
17471	↔¬¬⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 17469, 17470
17472	→↔¬¬⋀𝜑𝜓⋀𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓	Subs [𝜑↗↔¬¬⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17473	→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓	Modus ponens 17471, 17472
17474	↔→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗⋀𝜑𝜓] into pm5.74
17475	→↔→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓] into biimp
17476	→→𝜑↔¬¬⋀𝜑𝜓⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 17474, 17475
17477	↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 17473, 17476
17478	↔→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into pm5.74
17479	→↔→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑↔⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑⋀𝜑𝜓→𝜑𝜓] into biimp
17480	→→𝜑↔⋀𝜑𝜓𝜓↔→𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 17478, 17479
17481	→↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into biimp
17482	→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 17477, 17481
17483	→→→𝜑⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into ax-1
17484	→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6193, 17483
17485	→→→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17486	→→→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Modus ponens 17484, 17485
17487	→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Modus ponens 17482, 17486
17488	→↔→𝜑⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1
17489	→↔→𝜑¬¬⋀𝜑𝜓→𝜑⋀𝜑𝜓↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓] into bicom1
17490	↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17477, 17489
17491	→↔→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→𝜑⋀𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into biimp
17492	→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17490, 17491
17493	→→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into ax-1
17494	→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17492, 17493
17495	→→→𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2
17496	→→→𝜑𝜓→𝜑⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17494, 17495
17497	→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens ancl, 17496
17498	→→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into impbi
17499	→→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Modus ponens 17487, 17498
17500	↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Modus ponens 17497, 17499
17501	↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗𝜓] into pm5.74
17502	→↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓	Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓] into bicom1
17503	↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓	Modus ponens 17501, 17502
17504	→↔↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓	Subs [𝜑↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓, 𝜓↗→𝜑↔¬¬⋀𝜑𝜓𝜓] into biimp
17505	→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→𝜑↔¬¬⋀𝜑𝜓𝜓	Modus ponens 17503, 17504
17506	→𝜑↔¬¬⋀𝜑𝜓𝜓	Modus ponens 17500, 17505
17507	→↔→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓] into biimp
17508	→→𝜑↔¬¬⋀𝜑𝜓𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Modus ponens 17501, 17507
17509	→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into biimp
17510	→→→𝜑𝜓→𝜑¬¬𝜓→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑¬¬𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into ax-1
17511	→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓	Modus ponens 4585, 17510
17512	→→→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬𝜓→→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬¬𝜓] into ax-2
17513	→→→𝜑¬¬⋀𝜑𝜓→𝜑𝜓→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓	Modus ponens 17511, 17512
17514	→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓	Modus ponens 17487, 17513
17515	→↔→𝜑¬¬⋀𝜑𝜓→𝜑𝜓↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑𝜓] into bicom1
17516	↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17500, 17515
17517	→↔→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→𝜑𝜓, 𝜓↗→𝜑¬¬⋀𝜑𝜓] into biimp
17518	→→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into ax-1
17519	→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17497, 17518
17520	→→→𝜑¬¬𝜓→→𝜑𝜓→𝜑¬¬⋀𝜑𝜓→→→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→𝜑¬¬𝜓, 𝜓↗→𝜑𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2
17521	→→→𝜑¬¬𝜓→𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17519, 17520
17522	→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 4598, 17521
17523	→→→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓	Subs [𝜑↗→𝜑¬¬⋀𝜑𝜓, 𝜓↗→𝜑¬¬𝜓] into impbi
17524	→→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓	Modus ponens 17514, 17523
17525	↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓	Modus ponens 17522, 17524
17526	↔→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓	Subs [𝜓↗¬¬⋀𝜑𝜓, 𝜒↗¬¬𝜓] into pm5.74
17527	→↔→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓	Subs [𝜑↗→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓] into bicom1
17528	↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓	Modus ponens 17526, 17527
17529	→↔↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓	Subs [𝜑↗↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓, 𝜓↗→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓] into biimp
17530	→↔→𝜑¬¬⋀𝜑𝜓→𝜑¬¬𝜓→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓	Modus ponens 17528, 17529
17531	→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓	Modus ponens 17525, 17530
17532	↔↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into bicom
17533	→↔↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗↔¬¬𝜓¬¬⋀𝜑𝜓] into biimp
17534	→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17532, 17533
17535	→→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17536	→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17534, 17535
17537	→→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓↔¬¬𝜓¬¬⋀𝜑𝜓→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜓↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗↔¬¬𝜓¬¬⋀𝜑𝜓] into ax-2
17538	→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17536, 17537
17539	→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17531, 17538
17540	→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬⋀𝜑𝜓] into biimp
17541	→→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17542	→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17540, 17541
17543	→→𝜑→↔¬¬𝜓¬¬⋀𝜑𝜓→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜓↗↔¬¬𝜓¬¬⋀𝜑𝜓, 𝜒↗→¬¬𝜓¬¬⋀𝜑𝜓] into ax-2
17544	→→𝜑↔¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17542, 17543
17545	→𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17539, 17544
17546	→¬¬𝜓→𝜑¬¬𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑] into ax-1
17547	→→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓	Subs [𝜑↗→¬¬𝜓→𝜑¬¬𝜓, 𝜓↗¬¬𝜓] into ax-1
17548	→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓	Modus ponens 17546, 17547
17549	→→¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓→→¬¬𝜓¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗¬¬𝜓, 𝜒↗→𝜑¬¬𝜓] into ax-2
17550	→→¬¬𝜓¬¬𝜓→¬¬𝜓→𝜑¬¬𝜓	Modus ponens 17548, 17549
17551	→→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜓↗¬¬𝜓, 𝜒↗¬¬⋀𝜑𝜓] into ax-2
17552	→→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into ax-1
17553	→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17522, 17552
17554	→→¬¬𝜓→→𝜑¬¬𝜓→𝜑¬¬⋀𝜑𝜓→→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗→𝜑¬¬𝜓, 𝜒↗→𝜑¬¬⋀𝜑𝜓] into ax-2
17555	→→¬¬𝜓→𝜑¬¬𝜓→¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17553, 17554
17556	→¬¬𝜓→𝜑¬¬⋀𝜑𝜓	Modus ponens 17546, 17555
17557	→→¬¬𝜓→𝜑¬¬⋀𝜑𝜓→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗¬¬𝜓, 𝜓↗𝜑, 𝜒↗¬¬⋀𝜑𝜓] into ax-2
17558	→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17556, 17557
17559	→→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜑↗→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17560	→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17558, 17559
17561	→→𝜑→→¬¬𝜓𝜑→¬¬𝜓¬¬⋀𝜑𝜓→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Subs [𝜓↗→¬¬𝜓𝜑, 𝜒↗→¬¬𝜓¬¬⋀𝜑𝜓] into ax-2
17562	→→𝜑→¬¬𝜓𝜑→𝜑→¬¬𝜓¬¬⋀𝜑𝜓	Modus ponens 17560, 17561
17563	→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗¬𝜓, 𝜓↗¬⋀𝜑𝜓] into ax-3
17564	→→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17565	→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓	Modus ponens 17563, 17564
17566	→→𝜑→→¬¬𝜓¬¬⋀𝜑𝜓→¬⋀𝜑𝜓¬𝜓→→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬⋀𝜑𝜓¬𝜓	Subs [𝜓↗→¬¬𝜓¬¬⋀𝜑𝜓, 𝜒↗→¬⋀𝜑𝜓¬𝜓] into ax-2
17567	→→𝜑→¬¬𝜓¬¬⋀𝜑𝜓→𝜑→¬⋀𝜑𝜓¬𝜓	Modus ponens 17565, 17566
17568	→𝜑→¬⋀𝜑𝜓¬𝜓	Modus ponens 17545, 17567
17569	→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓	Subs [𝜑↗¬¬⋀𝜑𝜓, 𝜓↗¬¬𝜓] into biimp
17570	→→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓	Subs [𝜑↗→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓, 𝜓↗𝜑] into ax-1
17571	→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓	Modus ponens 17569, 17570
17572	→→𝜑→↔¬¬⋀𝜑𝜓¬¬𝜓→¬¬⋀𝜑𝜓¬¬𝜓→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬¬⋀𝜑𝜓¬¬𝜓	Subs [𝜓↗↔¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗→¬¬⋀𝜑𝜓¬¬𝜓] into ax-2
17573	→→𝜑↔¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬¬⋀𝜑𝜓¬¬𝜓	Modus ponens 17571, 17572
17574	→𝜑→¬¬⋀𝜑𝜓¬¬𝜓	Modus ponens 17531, 17573
17575	→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬𝜓] into ax-3
17576	→→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17577	→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓	Modus ponens 17575, 17576
17578	→→𝜑→→¬¬⋀𝜑𝜓¬¬𝜓→¬𝜓¬⋀𝜑𝜓→→𝜑→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬⋀𝜑𝜓	Subs [𝜓↗→¬¬⋀𝜑𝜓¬¬𝜓, 𝜒↗→¬𝜓¬⋀𝜑𝜓] into ax-2
17579	→→𝜑→¬¬⋀𝜑𝜓¬¬𝜓→𝜑→¬𝜓¬⋀𝜑𝜓	Modus ponens 17577, 17578
17580	→𝜑→¬𝜓¬⋀𝜑𝜓	Modus ponens 17574, 17579
17581	→→¬⋀𝜑𝜓¬𝜓→→¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗¬⋀𝜑𝜓, 𝜓↗¬𝜓] into impbi
17582	→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗→¬𝜓¬⋀𝜑𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1
17583	→→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓	Subs [𝜑↗→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17584	→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓	Modus ponens 17582, 17583
17585	→→𝜑→→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→𝜑→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓	Subs [𝜓↗→¬𝜓¬⋀𝜑𝜓, 𝜒↗→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓] into ax-2
17586	→→𝜑→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓	Modus ponens 17584, 17585
17587	→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓	Modus ponens 17580, 17586
17588	→→→¬⋀𝜑𝜓¬𝜓→→¬𝜓¬⋀𝜑𝜓↔¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬𝜓¬⋀𝜑𝜓, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2
17589	→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17581, 17588
17590	→→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17591	→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17589, 17590
17592	→→𝜑→→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓	Subs [𝜓↗→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓, 𝜒↗→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓] into ax-2
17593	→→𝜑→→¬⋀𝜑𝜓¬𝜓→¬𝜓¬⋀𝜑𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17591, 17592
17594	→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17587, 17593
17595	→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓] into id
17596	→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17597	→→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1
17598	→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓	Modus ponens 17596, 17597
17599	→→→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑→¬⋀𝜑𝜓¬𝜓] into ax-2
17600	→→→¬⋀𝜑𝜓¬𝜓→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓	Modus ponens 17598, 17599
17601	→→𝜑→→¬⋀𝜑𝜓¬𝜓↔¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2
17602	→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17594, 17601
17603	→→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗→¬⋀𝜑𝜓¬𝜓] into ax-1
17604	→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17602, 17603
17605	→→→¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→¬⋀𝜑𝜓¬𝜓, 𝜓↗→𝜑→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2
17606	→→→¬⋀𝜑𝜓¬𝜓→𝜑→¬⋀𝜑𝜓¬𝜓→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17604, 17605
17607	→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17596, 17606
17608	→→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17609	→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17607, 17608
17610	→→𝜑→→¬⋀𝜑𝜓¬𝜓→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜓↗→¬⋀𝜑𝜓¬𝜓, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2
17611	→→𝜑→¬⋀𝜑𝜓¬𝜓→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17609, 17610
17612	→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17568, 17611
17613	→→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜓↗𝜑, 𝜒↗↔¬⋀𝜑𝜓¬𝜓] into ax-2
17614	→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17612, 17613
17615	→→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜑↗→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗𝜑] into ax-1
17616	→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17614, 17615
17617	→→𝜑→→𝜑𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓→→𝜑→𝜑𝜑→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔¬⋀𝜑𝜓¬𝜓] into ax-2
17618	→→𝜑→𝜑𝜑→𝜑→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens 17616, 17617
17619	→𝜑↔¬⋀𝜑𝜓¬𝜓	Modus ponens id, 17614
17620	↔→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓	Subs [𝜓↗¬⋀𝜑𝜓, 𝜒↗¬𝜓] into pm5.32
17621	→↔→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓→→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓	Subs [𝜑↗→𝜑↔¬⋀𝜑𝜓¬𝜓, 𝜓↗↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓] into biimp
17622	→→𝜑↔¬⋀𝜑𝜓¬𝜓↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓	Modus ponens 17620, 17621
17623	↔⋀𝜑¬⋀𝜑𝜓⋀𝜑¬𝜓	Modus ponens 17619, 17622	annotanannot
17624	→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜓] into biimp
17625	→→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓	Subs [𝜑↗→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
17626	→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓	Modus ponens 17624, 17625
17627	→→𝜑→↔⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜓→→𝜑↔⋀𝜑𝜓𝜓→𝜑→⋀𝜑𝜓𝜓	Subs [𝜓↗↔⋀𝜑𝜓𝜓, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
17628	→→𝜑↔⋀𝜑𝜓𝜓→𝜑→⋀𝜑𝜓𝜓	Modus ponens 17626, 17627
17629	→𝜑→⋀𝜑𝜓𝜓	Modus ponens 8176, 17628
17630	→⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17631	→→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗→⋀𝜑𝜓→𝜑⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
17632	→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 17630, 17631
17633	→→⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗⋀𝜑𝜓, 𝜒↗→𝜑⋀𝜑𝜓] into ax-2
17634	→→⋀𝜑𝜓⋀𝜑𝜓→⋀𝜑𝜓→𝜑⋀𝜑𝜓	Modus ponens 17632, 17633
17635	→→𝜑→⋀𝜑𝜓𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜓↗⋀𝜑𝜓, 𝜒↗𝜓] into ax-2
17636	→→→𝜑⋀𝜑𝜓→𝜑𝜓→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗→→𝜑⋀𝜑𝜓→𝜑𝜓, 𝜓↗⋀𝜑𝜓] into ax-1
17637	→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓	Modus ponens 6193, 17636
17638	→→⋀𝜑𝜓→→𝜑⋀𝜑𝜓→𝜑𝜓→→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→𝜑𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗→𝜑⋀𝜑𝜓, 𝜒↗→𝜑𝜓] into ax-2
17639	→→⋀𝜑𝜓→𝜑⋀𝜑𝜓→⋀𝜑𝜓→𝜑𝜓	Modus ponens 17637, 17638
17640	→𝜑→⋀𝜑𝜓𝜑	Subs [𝜓↗⋀𝜑𝜓] into ax-1
17641	→→𝜑→⋀𝜑𝜓𝜑→𝜑→𝜑→⋀𝜑𝜓𝜑	Subs [𝜑↗→𝜑→⋀𝜑𝜓𝜑, 𝜓↗𝜑] into ax-1
17642	→𝜑→𝜑→⋀𝜑𝜓𝜑	Modus ponens 17640, 17641
17643	→→𝜑→𝜑→⋀𝜑𝜓𝜑→→𝜑𝜑→𝜑→⋀𝜑𝜓𝜑	Subs [𝜓↗𝜑, 𝜒↗→⋀𝜑𝜓𝜑] into ax-2
17644	→→𝜑𝜑→𝜑→⋀𝜑𝜓𝜑	Modus ponens 17642, 17643
17645	→→⋀𝜑𝜓→𝜑𝜓→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜑, 𝜒↗𝜓] into ax-2
17646	→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓	Modus ponens pm3.4, 17645
17647	→→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓	Subs [𝜑↗→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
17648	→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓	Modus ponens 17646, 17647
17649	→→𝜑→→⋀𝜑𝜓𝜑→⋀𝜑𝜓𝜓→→𝜑→⋀𝜑𝜓𝜑→𝜑→⋀𝜑𝜓𝜓	Subs [𝜓↗→⋀𝜑𝜓𝜑, 𝜒↗→⋀𝜑𝜓𝜓] into ax-2
17650	→→𝜑→⋀𝜑𝜓𝜑→𝜑→⋀𝜑𝜓𝜓	Modus ponens 17648, 17649
17651	→→→𝜒𝜒→𝜓→𝜒𝜒→𝜑→→𝜒𝜒→𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1
17652	→𝜑→→𝜒𝜒→𝜓→𝜒𝜒	Modus ponens 51, 17651
17653	→→𝜑→→𝜒𝜒→𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→𝜓→𝜒𝜒	Subs [𝜓↗→𝜒𝜒, 𝜒↗→𝜓→𝜒𝜒] into ax-2
17654	→→𝜑→𝜒𝜒→𝜑→𝜓→𝜒𝜒	Modus ponens 17652, 17653
17655	→𝜑→𝜓→𝜒𝜒	Modus ponens 815, 17654
17656	→→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
17657	→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒	Modus ponens 57, 17656
17658	→→𝜑→→𝜓→𝜒𝜒→→𝜓𝜒→𝜓𝜒→→𝜑→𝜓→𝜒𝜒→𝜑→→𝜓𝜒→𝜓𝜒	Subs [𝜓↗→𝜓→𝜒𝜒, 𝜒↗→→𝜓𝜒→𝜓𝜒] into ax-2
17659	→→𝜑→𝜓→𝜒𝜒→𝜑→→𝜓𝜒→𝜓𝜒	Modus ponens 17657, 17658
17660	→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓	Subs [𝜑↗→⋀𝜑𝜓𝜓, 𝜓↗→𝜓𝜒] into ax-1
17661	→→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓	Subs [𝜑↗→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓, 𝜓↗𝜑] into ax-1
17662	→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓	Modus ponens 17660, 17661
17663	→→𝜑→→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜑→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓	Subs [𝜓↗→⋀𝜑𝜓𝜓, 𝜒↗→→𝜓𝜒→⋀𝜑𝜓𝜓] into ax-2
17664	→→𝜑→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓	Modus ponens 17662, 17663
17665	→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓	Modus ponens 17629, 17664
17666	→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Subs [𝜑↗𝜓, 𝜓↗𝜒, 𝜒↗⋀𝜑𝜓] into imim2
17667	→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜓↗→𝜓𝜒] into ax-1
17668	→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Modus ponens 17666, 17667
17669	→→→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→𝜓𝜒, 𝜒↗→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒] into ax-2
17670	→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Modus ponens 17668, 17669
17671	→→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Subs [𝜑↗→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17672	→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Modus ponens 17670, 17671
17673	→→𝜑→→→𝜓𝜒→𝜓𝜒→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Subs [𝜓↗→→𝜓𝜒→𝜓𝜒, 𝜒↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒] into ax-2
17674	→→𝜑→→𝜓𝜒→𝜓𝜒→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Modus ponens 17672, 17673
17675	→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒	Modus ponens 869, 17674
17676	→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜓, 𝜒↗→⋀𝜑𝜓𝜒] into ax-2
17677	→→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17678	→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17676, 17677
17679	→→𝜑→→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17680	→→𝜑→→𝜓𝜒→→⋀𝜑𝜓𝜓→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17678, 17679
17681	→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17675, 17680
17682	→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜓→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜓, 𝜒↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17683	→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜓→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17681, 17682
17684	→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17665, 17683
17685	→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓	Subs [𝜑↗𝜓, 𝜓↗⋀𝜑𝜓] into biimp
17686	→→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓	Subs [𝜑↗→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17687	→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓	Modus ponens 17685, 17686
17688	→→𝜑→↔𝜓⋀𝜑𝜓→𝜓⋀𝜑𝜓→→𝜑↔𝜓⋀𝜑𝜓→𝜑→𝜓⋀𝜑𝜓	Subs [𝜓↗↔𝜓⋀𝜑𝜓, 𝜒↗→𝜓⋀𝜑𝜓] into ax-2
17689	→→𝜑↔𝜓⋀𝜑𝜓→𝜑→𝜓⋀𝜑𝜓	Modus ponens 17687, 17688
17690	→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒	Subs [𝜑↗→𝜒𝜒, 𝜓↗⋀𝜑𝜓] into ax-1
17691	→→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒	Subs [𝜑↗→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒, 𝜓↗𝜑] into ax-1
17692	→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒	Modus ponens 17690, 17691
17693	→→𝜑→→𝜒𝜒→⋀𝜑𝜓→𝜒𝜒→→𝜑→𝜒𝜒→𝜑→⋀𝜑𝜓→𝜒𝜒	Subs [𝜓↗→𝜒𝜒, 𝜒↗→⋀𝜑𝜓→𝜒𝜒] into ax-2
17694	→→𝜑→𝜒𝜒→𝜑→⋀𝜑𝜓→𝜒𝜒	Modus ponens 17692, 17693
17695	→𝜑→⋀𝜑𝜓→𝜒𝜒	Modus ponens 815, 17694
17696	→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒] into ax-2
17697	→→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17698	→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17696, 17697
17699	→→𝜑→→⋀𝜑𝜓→𝜒𝜒→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→⋀𝜑𝜓→𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗→⋀𝜑𝜓→𝜒𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17700	→→𝜑→⋀𝜑𝜓→𝜒𝜒→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17698, 17699
17701	→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17695, 17700
17702	→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓	Subs [𝜑↗→𝜓⋀𝜑𝜓, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
17703	→→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓	Subs [𝜑↗→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓, 𝜓↗𝜑] into ax-1
17704	→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓	Modus ponens 17702, 17703
17705	→→𝜑→→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→𝜑→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓	Subs [𝜓↗→𝜓⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓] into ax-2
17706	→→𝜑→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓	Modus ponens 17704, 17705
17707	→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓	Modus ponens pm3.2, 17706
17708	→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Subs [𝜑↗⋀𝜑𝜓, 𝜓↗𝜒, 𝜒↗𝜓] into imim2
17709	→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into ax-1
17710	→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Modus ponens 17708, 17709
17711	→→→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒, 𝜒↗→→𝜓⋀𝜑𝜓→𝜓𝜒] into ax-2
17712	→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Modus ponens 17710, 17711
17713	→→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Subs [𝜑↗→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜓↗𝜑] into ax-1
17714	→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Modus ponens 17712, 17713
17715	→→𝜑→→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Subs [𝜓↗→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒] into ax-2
17716	→→𝜑→→⋀𝜑𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Modus ponens 17714, 17715
17717	→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒	Modus ponens 17701, 17716
17718	→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→⋀𝜑𝜓𝜒, 𝜓↗→𝜓⋀𝜑𝜓, 𝜒↗→𝜓𝜒] into ax-2
17719	→→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
17720	→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 17718, 17719
17721	→→𝜑→→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜓↗→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒, 𝜒↗→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
17722	→→𝜑→→⋀𝜑𝜓𝜒→→𝜓⋀𝜑𝜓→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 17720, 17721
17723	→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 17717, 17722
17724	→→𝜑→→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓, 𝜒↗→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
17725	→→𝜑→→⋀𝜑𝜓𝜒→𝜓⋀𝜑𝜓→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 17723, 17724
17726	→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜓𝜒, 𝜓↗→⋀𝜑𝜓𝜒] into impbi
17727	→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1
17728	→→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜑↗→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜓↗𝜑] into ax-1
17729	→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 17727, 17728
17730	→→𝜑→→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Subs [𝜓↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒] into ax-2
17731	→→𝜑→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 17729, 17730
17732	→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒	Modus ponens 4703, 17731
17733	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→⋀𝜑𝜓𝜒→𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17734	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17726, 17733
17735	→→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17736	→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17734, 17735
17737	→→𝜑→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒, 𝜒↗→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17738	→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→→⋀𝜑𝜓𝜒→𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17736, 17737
17739	→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17732, 17738
17740	→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into id
17741	→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17742	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1
17743	→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17741, 17742
17744	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17745	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17743, 17744
17746	→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17747	→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17739, 17746
17748	→→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-1
17749	→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17747, 17748
17750	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17751	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17749, 17750
17752	→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17741, 17751
17753	→→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17754	→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17752, 17753
17755	→→𝜑→→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗→→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17756	→→𝜑→→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17754, 17755
17757	→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17684, 17756
17758	→→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗𝜑, 𝜒↗↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17759	→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17757, 17758
17760	→→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜑↗→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗𝜑] into ax-1
17761	→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17759, 17760
17762	→→𝜑→→𝜑𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Subs [𝜓↗→𝜑𝜑, 𝜒↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒] into ax-2
17763	→→𝜑→𝜑𝜑→𝜑→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens 17761, 17762
17764	→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒	Modus ponens id, 17759
17765	↔→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒	Subs [𝜓↗→𝜓𝜒, 𝜒↗→⋀𝜑𝜓𝜒] into pm5.32
17766	→↔→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒→→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒	Subs [𝜑↗→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒, 𝜓↗↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒] into biimp
17767	→→𝜑↔→𝜓𝜒→⋀𝜑𝜓𝜒↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒	Modus ponens 17765, 17766
17768	↔⋀𝜑→𝜓𝜒⋀𝜑→⋀𝜑𝜓𝜒	Modus ponens 17764, 17767	pm5.33